JEE MATHEMATICS MCQ: SYSTEM OF CIRCLES

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Application +4 | -1

If a chord of a circle

x^2+y^2=25

with one extremity at

(4,3)

subtends a right angle at the centre of this circle, then the coordinates of the other extremity of this chord can be.

View answer and explanation

Correct option: D

(-3,4)

Option D ((-3,4)) is correct because the dot product of the position vectors of the two extremities of the chord is zero, indicating a right angle at the center.

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x = 1

is the radical axis of the two orthogonally intersecting circles. If

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

is one of the circles, then the other circle is The circle

{x^2} + {y^2} + 8y - 4 = 0

, cuts the real circle

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

orthogonally, if The equation of the circle whose diameter is the common chord of the circles

x^2+y^2+3 x+2 y+1=0

and

x^2+y^2+3 x+4 y+2=0

, is If the circles

{x^2} + {y^2} + 2ky + 2x + 6 = 0

and

{x^2} + {y^2} + 2ky + k = 0

intersects orthogonally. Then, the value of

k

is If the circles

x^2+y^2+2 a x+c y+a=0

and

x^2+y^2-3 a x+d y-1=0

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P

and

Q

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5 x+b y-a=0

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P

and

Q

for The equation of the circle having its centre on the line

x + 2y - 3 = 0

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{x^2} + {y^2} - 4y + 1 = 0

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