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JEE MATHEMATICS MCQ: CIRCLES

1 Easy

1 of 1

Application +4 | -1

The locus of a point from which the length of tangents to the circles

x^2+y^2=4

and

2\left(x^2+y^2\right)-10 x+3 y-2=0

are equal is

View answer and explanation

Correct option: D

A straight line perpendicular to the line joining the centres of the circles

Option D (A straight line perpendicular to the line joining the centres of the circles) is correct because the locus of points from which the lengths of tangents to two circles are equal is the radical axis, which is a straight line perpendicular to the line joining the centers of the circles.

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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