Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 105

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IMPORTANT

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A normal of slope $1$ of ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ meets the major and minor axes at $P$ and $Q$ respectively. If $C$ be the centre of ellipse, then the area of $Δ C P Q$ is

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Important Questions on Conic Section

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 106

An ellipse is described by using an endless string which is passed over two pins. If the axes are

6 cm

and

4 cm,

the necessary length of the string and the distance between the pins respectively in

cm,

are

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 107

If a tangent having slope of

- \frac{4}{3}

to the ellipse

\frac{x^{2}}{18} + \frac{y^{2}}{32} = 1

intersects the major and minor axes in points

A

and

B

respectively, then the area of

Δ O A B

is equal to -

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 108

If the eccentric angles of the extremities of a chord of an ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ are $α$ and $β$ and if the chord cuts the major axis at a distance $c$ from centre, then $\tan (\frac{α}{2}) \tan (\frac{β}{2})$ is equal to

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 109

A set of points is such that each point is three times as far away from the

y

-axis as it is from the point

(4, 0)

. Then the locus of the points is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 110

Length of latus rectum of the ellipse

2 x^{2} + y^{2} - 8 x + 2 y + 7 = 0

is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 111

Locus of the point of intersection of the tangents at the end points of the focal chord of an ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, (b < a)

is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 112

Perpendiculars $A B$ and $A C$ are drawn from point $A$ to straight lines $O B$ and $O C .$ If the area of $O B A C$ is constant, then locus of $A$ is