Let … be a point on the parabola … such that the tangent at … passes through the centre of the circle …. Let … be the product of all possible values of … and … be the product of all possible values of …. Then the value of … is equal to :

Option D. Centre of circle … is at (5, 7).

Parabola

JEE Main 2022 · 27 Jul, Morning shift · Q4751

MathematicsMedium92×since 2002Q4751

Let

P(a, b)

be a point on the parabola

y^{2}=8 x

such that the tangent at

P

passes through the centre of the circle

x^{2}+y^{2}-10 x-14 y+65=0

. Let

A

be the product of all possible values of

a

and

B

be the product of all possible values of

b

. Then the value of

A+B

is equal to :

JEE Main 2022 · 27 Jul, Morning shift · Q4751

MathematicsMedium92×since 2002Q4751

Let

P(a, b)

be a point on the parabola

y^{2}=8 x

such that the tangent at

P

passes through the centre of the circle

x^{2}+y^{2}-10 x-14 y+65=0

. Let

A

be the product of all possible values of

a

and

B

be the product of all possible values of

b

. Then the value of

A+B

is equal to :