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An ellipse with major and minor axes length as $2 a$ and $2 b$ touches coordinate axes in first quadrant and having foci $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ then the value of $x_{1} x_{2}$ and $y_{1} y_{2}$ is

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Important Questions on Conic Section

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 12 - Conic Section>Exercise>Q 58

Let

P_{i}

and

{P_{i}}^{'}

be the feet of the perpendiculars drawn from foci

S,

S^{'}

on a tangent

T_{i}

to an ellipse whose length of semi-major axis is

20,

\sum_{i = 1}^{10} (S P_{i}) (S^{'} P_{i}^{'}) = 2560,

then the value of eccentricity is

HARD

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IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 12 - Conic Section>Exercise>Q 59

If maximum distance of any point on the ellipse

x^{2} + 2 y^{2} + 2 x y = 1

from its centre be

r,

then

r

is equal to

HARD

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IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 12 - Conic Section>Exercise>Q 60

The set of values of

m

for which it is possible to draw the chord

y = \sqrt{m} x + 1

to the curve

x^{2} + 2 x y + (2 + \sin^{2} α) y^{2} = 1,

which subtends a right angle at the origin for some value of

α

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 12 - Conic Section>Exercise>Q 61

If the distance between the foci and the distance between the two directrix of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

are in the ratio

3 : 2,

then

b : a

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 12 - Conic Section>Exercise>Q 62

A tangent drawn to hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

P (\frac{π}{6})

forms a triangle of area

3 a^{2} sq . units

, with coordinate axes, then the square of its eccentricity is

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 12 - Conic Section>Exercise>Q 63

A straight line has its extremities on two fixed perpendicular straight lines and cuts off from them a triangle of constant area

c^{2} .

Then the locus of the middle point of the line is

HARD

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IMPORTANT

Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 12 - Conic Section>Exercise>Q 64

If a variable line has its intercepts on the coordinate axes as

e and e',

where

\frac{e}{2}, \frac{e'}{2}

are the eccentricities of a hyperbola and its conjugate hyperbola, then the line always touches the circle

x^{2} + y^{2} = r^{2},

where

r =

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Practice Book for KVPY Aptitude Test - Stream SA Mathematics>Chapter 12 - Conic Section>Exercise>Q 65

The equation of the transverse axis of the hyperbola

(x - 3)^{2} + (y + 1)^{2} = (4 x + 3 y)^{2}

An ellipse with major and minor axes length as 2a and 2b touches coordinate axes in first quadrant and having foci x1,y1 and x2,y2 then the value of x1x2 and y1y2 is

Important Questions on Conic Section

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An ellipse with major and minor axes length as $2 a$ and $2 b$ touches coordinate axes in first quadrant and having foci $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ then the value of $x_{1} x_{2}$ and $y_{1} y_{2}$ is