Circles Test - ...

The locus of the centre of a circle which cuts off intercepts of length 2a and 2b from x-axis and y-axis respectively, is

Two perpendicular tangents to the circle x²+y²=r² meet at P. The locus of P is

In the given figure, AB is the diameter of the largest circle, P and Q are centres of the two small circles touching the largest circle at points A and B, respectively. The small circles touch each other externally at point M. What is the radius of the small circle with centre Q?

If (x-a)² + (y-b)² = c² represents a circle, then

The area of the circle in which a chord of length √2 makes an angle π/2 at the centre is

Circumcentre of the triangle, whose vertices are (0, 0), (6, 0) and (0, 4) is

The director circle is the locus of the point of intersection of

The area of the circle with centre at (1, 2) and passing through (4, 6) is

The circles whose equations are x² + y² + c² = 2ax, and x² + y² + c² – 2by = 0 will touch each other externally if

What will be the locus of point whose distance from the point (–g, –f) is always 'a'? (Given k = g² + f² – a²)

x = a cos t, y = a sin t is the parametric form of a/an 

O is the centre of the given circle and PR is the diameter. AT is the tangent to the circle at point A. What is the measure of PQR?

A circle passes through the origin and cuts intercepts a and b on the axes. The equation of the circle is 

The area of a circle with centre (h, k) and radius a is

If the centre of a circle is (2, 3) and a tangent to the circle is x + y = 1, then the equation of this circle is

Find the center and the radius of the circle (x + 5)² + (y + 7)² = 36.

The equation of a circle with centre (4, 3) and touching the circle x² + y² = 1, is

A circle is inscribed in an equilateral triangle of side a. The area of any square inscribed in the circle is

The length of the chord joining the point ( 4 cos θ, 4 sin θ) and 4 ( cos(θ+60^o), 4 sin(θ + 60^o)) of the circle x²+y²=16 is

Let C be any circle with centre (0, ). How many rational points are there on C?

The number of tangents to the circle x²+y²−8x−6y+9=0, which pass through the point ( 3, - 2), is

The number of tangents which can be drawn from the point (– 1, 2) to the circle x² + y² + 2x – 4y + 4 = 0 is

In the given figure, O is the centre of the circle and PQ is a tangent to the circle at P.



If OP = 3 cm and PQ = 12 cm, then what is the length of OQ?

The value of k, such that the equation  2x²+2y²−6x+8y+k=0 represents a point circle, is

Which of the following statements is true for the two circles x² + y² – 4y = 0 and x² + y² – 8y = 0?

If the equation x² + 2gx + 2fy + c = 0 represents a circle with x-axis as a diameter and radius a, then