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JEE MATHEMATICS MCQ: PARABOLA

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Application +4 | -1

Tangents drawn from the point

\left( {c,d} \right)

to the hyperbola

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

make angles

\alpha

and

\beta

with the

x

-axis. If

\tan \alpha \tan \beta = 1,

then

{c^2} - {d^2} =

View answer and explanation

Correct option: C

{a^2} + {b^2}

Option C (

{a^2} + {b^2}

) is correct because the condition

\tan \alpha \tan \beta = 1

leads to the relationship

{c^2} - {d^2} = {a^2} + {b^2}

.

More Questions from PARABOLA

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The equation of a common tangent to the parabolas

y=x^2

y=-(x-2)^2

P

moves such that slope of one tangent drawn from it to parabola

y^2=16 x

is four times the slope of other tangent, then the length of latus rectum of the conic represented by locus of

P

P,Q,R

be three points on parabola

{y^2} = 4x

P

R

Q

, then the locus of the mid-point of the chord

PR

is a parabola whose vertex is at The tangents at the end points of any chord through

(1,0)

to the parabola

y^2+4 x=8

intersect The focus of the parabola

x^2=-16 y

I

denotes the semi-latusrectum of the parabola

{y^2} = 4ax

SP

SQ

denote the segments of any focal chord

PQ,S

being the focus, then

SP,l

SQ

are in the relation