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JEE MATHEMATICS MCQ: CIRCLES

1 Easy

1 of 1

Application +4 | -1

If the line

y=x+3

meets the circle

x^2+y^2=a^2

at

A

and

B

, then equation of the circle on

A B

as diameter is

View answer and explanation

Correct option: A

x^2+y^2+3 x-3 y-a^2+9=0

Option A (

x^2+y^2+3x-3y-a^2+9=0

) is correct because the equation of the circle on AB as diameter can be found by considering the family of circles passing through the intersection of the given circle and line, and then using the condition that the center of the circle lies on the given line.

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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)

\quad \alpha, \beta

\gamma

are the parametric angles of three points

P, Q

, and R respectively, on the circle

x^2+y^2=1

A

(-1,0)

. If the lengths of the chords

A P, A Q

A R

G P

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

\cos \gamma / 2

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

x+y=6

x+2 y=4

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

x+y=5

x-y=1

9 \pi

, then the equation of the circle is