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Class XI Maths Circles 1

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Question 1

If the radical axis of the circles x² + y² + 2gx + 2fy + c = 0 and 2x² + 2y² + 3x + 8y + 2c = 0 touches the circle x² + y² + 2x + 2y + 1 = 0, then

Question 2

The radical centre of three circles described on the three sides of a triangle as diameter is the

Question 3

The polar of the point (5, –1/2) with respect to the circle (x – 2)² + y² = 4 is-

Question 4

The polar of a point with respect to the circle x² + y² – 2ηx + c² = 0 -

Question 5

If a line is drawn through a fixed point P(α, β) to cut the circle x² + y² = a² at A and B, then PA . PB =

Question 6

Let φ (x, y) = 0 be the equation of a circle. If φ (0, η) = 0 has equal roots η = 2, 2 and φ (η, 0) = 0 has roots η =

, 5 then the centre of the circle is –

Question 7

The equation of the circle of radius 2√2 whose centre lies on the line x – y = 0 and which touches the line x + y = 4, and whose centre's coordinates satisfy the inequality x + y > 4 is

Question 8

The values of p for which the power of a point (2, 5) is negative with respect to circle x² + y² – 8x – 12y + p = 0 which neither touches the axis nor cuts them are

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Jan 22JEE & BITSAT