JEE MATHEMATICS MCQ: CIRCLES

1 Medium

1 of 1

Analyzing +4 | -1

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

View answer and explanation

Correct option: D

Option D (65) is correct because it is the sum of the product of all possible values of 'a' and the product of all possible values of 'b', where (a, b) lies on the parabola and the tangent at that point passes through the center of the given circle.

More Questions from CIRCLES

Practice All Chapter MCQs →

The sum of the coefficients in the expansion of

{\left( {{\alpha ^2}{x^2} - 2\alpha \mathrm{ }x + 1} \right)^{51}},

as a polynomial in

x

, vanishes. Position of the point

\left( {\alpha ,2{\alpha ^2}} \right)

with respect to the circle

{x^2} + {y^2} = 4,

is One of the diameter of the circle

{x^2} + {y^2} - 2x + 4y - 4 = 0

is The locus of the middle point of the chords of the circle

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

such that the chords pass through a given point

\left( {{x_1},{y_1}} \right)

, is

\quad \alpha, \beta

and

\gamma

are the parametric angles of three points

P, Q

, and R respectively, on the circle

x^2+y^2=1

, and

A

is the point

(-1,0)

. If the lengths of the chords

A P, A Q

and

A R

are in

G P

, then

\cos \alpha / 2, \cos \beta / 2

and

\cos \gamma / 2

are in The radius of the circle passing through the point (6,2), two of whose diameters are

x+y=6

and

x+2 y=4

is If a circle has two of its diameters along the lines

x+y=5

and

x-y=1

and has area

9 \pi

, then the equation of the circle is