## Question

### Solution

Correct option is Let OA = a and OB = b then the co-ordinates of A and B are

(a, 0) and (0, b) respectively.

Since             ∠AOB = π/2

Hence AB is the diameter of the required circle whose equation is  Equation of tangent at (0, 0) of (1) is or        ax + by = 0     Adding (2) and (3), we get From (2) and (3), we get From (1), equation of required circle is #### SIMILAR QUESTIONS

Q1 be a given circle. Find the locus of the foot of perpendicular drawn from origin upon any chord of Swhich subtends a right angle at the origin.

Q2 be a given circle. Find the locus of the foot of perpendicular drawn from origin upon any chord of Swhich subtends a right angle at the origin.

Q3

P is a variable on the line y = 4. Tangents are drawn to the circle x2 + y2= 4 from P to touch it at A and B. The perpendicular PAQB is completed. Find the equation of the locus of Q.

Q4

Find the condition on abc such that two chords of the circle

x2 + y2 – 2ax – 2by + a2 + b2 – c2 = 0

passing through the point (ab + c) are bisected by the line y = x.

Q5

Find the limiting points of the circles

(x2 + y2 + 2gx + c) + λ(x2 + y2 + 2fy + d) = 0

Q6

The circle x2 + y2 – 4x – 8y + 16 = 0 rolls up the tangent to it at by 2 units, assuming the x-axis as horizontal, find the equation of the circle in the new position.

Q7

Find the equation of the circle of minimum radius which contains the three circles

x2 – y2 – 4y – 5 = 0

x2 + y2 + 12x + 4y + 31 = 0

and         x2 + y2 + 6x + 12y + 36 = 0

Q8

Find the equation of the circle passing through (1, 0) and (0, 1) and having the smallest possible radius.

Q9

If the line x cos α + y sin α = p cuts the circle x2 + y2 = a2 in M and N, then show that the circle, whose diameter is MN, is Q10

Tangents PQPR are drawn to the circle x2 + y2 = 36 from the point P(–8, 2) touching the circle at QR respectively. Find the equation of the circumcircle of the âˆ†PQR.