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Mathematics · Class 11 Science

Ch 12Conic Sections — Class 11 Mathematics, concept-first.

A conic section (or simply a conic) is any curve obtained by intersecting a plane with a double right circular cone -- two identical cones placed apex to apex (called nappes), extending indefinitely in both directions along a common axis.

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Key concepts

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Sections of a Cone

Every conic section -- circle, ellipse, parabola or hyperbola -- is obtained by intersecting a plane with a double right circular cone, and which curve results depends entirely on the angle the cutting plane makes with t…

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Chapter contents

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Sections of a Cone

A conic section (or simply a conic) is any curve obtained by intersecting a plane with a double right circular cone -- two identical cones placed apex to apex (called nappes), extending indefinitely i…

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Standard Equation of a Circle

A circle is defined as the set (locus) of all points in a plane that lie at a fixed positive distance, called the radius , from a fixed point, called the centre.

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General Equation of a Circle

Expanding the standard equation gives which can be rewritten, after collecting terms, as This is the general equation of a circle -- the equation of every circle can be written this way, and (subject…

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Standard Equation and Properties of a Parabola

A parabola is defined as the locus of a point that moves so that its distance from a fixed point, the focus , always equals its (perpendicular) distance from a fixed straight line, the directrix, whic…

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Standard Equation and Properties of an Ellipse

An ellipse is defined as the locus of a point that moves so that the sum of its distances from two fixed points, the foci and , is always the same constant, (with greater than the distance between the…

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Standard Equation and Properties of a Hyperbola

A hyperbola is defined as the locus of a point that moves so that the absolute difference of its distances from two fixed points, the foci and , is always the same constant, (with less than the distan…

Summary

Conic sections (circle, ellipse, parabola, hyperbola) all arise from slicing a double right circular cone at different angles against its semi-vertical angle : gives a circle, an ellipse, a parabola,…

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+Show 3 questions3 questions
  1. Q31A double right circular cone with semi-vertical angle $\alpha$ is cut by a plane passing through the vertex $V$. State the degenerate conic…Free
  2. Q32Find the equation(s) of the circle(s) which touch the $x$-axis at the point $(3,0)$ and have radius $5$.Preview
  3. Q33A parabola always has eccentricity $e=1$. Using the ellipse relation $b^2=a^2(1-e^2)$ and the hyperbola relation $b^2=a^2(e^2-1)$, explain w…Preview
+Show 10 questions10 questions
  1. Example 1Find the equation of the circle with centre $(2,-3)$ and radius $5$.Free
  2. Example 2Find the centre and radius of the circle $x^2+y^2-6x+4y-12=0$.Free
  3. Example 3Find the equation of the circle passing through the points $(6,5)$ and $(-1,4)$, given that its centre lies on the line $x-y=2$.Free
  4. Example 4Find the coordinates of the focus, the equation of the directrix, the axis and the length of the latus rectum of the parabola $y^2=12x$.Preview
  5. Example 5Find the equation of the parabola with focus $(4,0)$ and directrix $x=-4$.Preview
  6. Example 6Find the equation of the parabola with vertex at the origin, axis along the $y$-axis, and passing through the point $(6,-3)$.Preview
  7. Example 7Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the ellipse $\dfrac{x^2}{25}+\dfrac{y…Preview
  8. Example 8Find the equation of the ellipse whose vertices are $(\pm10,0)$ and foci are $(\pm6,0)$.Preview
  9. Example 9Find the coordinates of the foci, the vertices, the eccentricity, the length of the latus rectum and the equations of the asymptotes of the…Preview
  10. Example 10Find the equation of the hyperbola with vertices $(0,\pm3)$ and foci $(0,\pm5)$.Preview
+Show 5 questions5 questions
  1. Q11Find the equation of the circle with centre $(0,0)$ and radius $7$.Free
  2. Q12Find the equation of the circle with centre $(-2,3)$ and radius $4$.Free
  3. Q13Find the centre and radius of the circle $x^2+y^2-4x-8y-5=0$.Preview
  4. Q14Find the centre and radius of the circle $2x^2+2y^2-x=0$.Preview
  5. Q15Find the equation of the circle which passes through the origin and has its centre at $(3,4)$.Preview
+Show 5 questions5 questions
  1. Q16Find the coordinates of the focus, the equation of the directrix, the axis and the length of the latus rectum of the parabola $y^2=8x$.Free
  2. Q17Find the coordinates of the focus, the equation of the directrix, the axis and the length of the latus rectum of the parabola $x^2=-16y$.Free
  3. Q18Find the equation of the parabola with focus $(0,-3)$ and directrix $y=3$.Preview
  4. Q19Find the equation of the parabola with vertex at the origin, axis along the $x$-axis, and passing through the point $(1,-2)$.Preview
  5. Q20Find the equation of the parabola with vertex at the origin, axis along the $y$-axis, and passing through the point $(4,4)$.Preview
+Show 5 questions5 questions
  1. Q21Find the coordinates of the foci, the vertices, the eccentricity, the lengths of the major and minor axes, and the length of the latus rectu…Free
  2. Q22Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the ellipse $4x^2+9y^2=36$.Free
  3. Q23Find the equation of the ellipse whose vertices are $(0,\pm13)$ and foci are $(0,\pm5)$.Preview
  4. Q24Find the equation of the ellipse whose length of the major axis is $20$ and foci are $(\pm4,0)$.Preview
  5. Q25Find the equation of the ellipse with semi-major axis $6$, eccentricity $\dfrac{2}{3}$, and major axis along the $x$-axis.Preview
+Show 5 questions5 questions
  1. Q26Find the coordinates of the foci, the vertices, the eccentricity, the length of the latus rectum and the equations of the asymptotes of the…Free
  2. Q27Find the coordinates of the foci, the vertices, the eccentricity and the equations of the asymptotes of the hyperbola $16y^2-9x^2=144$.Free
  3. Q28Find the equation of the hyperbola whose foci are $(\pm13,0)$ and the length of the transverse axis is $24$.Preview
  4. Q29Find the equation of the hyperbola whose vertices are $(0,\pm6)$ and eccentricity is $\dfrac{5}{3}$.Preview
  5. Q30Find the equation of the hyperbola whose foci are $(\pm13,0)$ and the length of the conjugate axis is $24$.Preview