Conic Sections ...

The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle of area 154 sq. units. The equation of the circle is

If a be the radius of a circle which touches x-axis at the origin, then its equation is

The equation of the circle passing through (3, 6) and whose centre is (2, –1) is

The equation of a circle which passes through the three points (3, 0) (1, –6), (4, –1) is

y = √3x + c₁  &y = √3x + c₂  are two parallel tangents of a circle of radius 2 units, then |c₁  – c₂ | is equal to

B and C are fixed point having co-ordinates (3, 0) and (–3, 0) respectively. If the vertical angle BAC is 90 º, then the locus of the centroid of the DABC has the equation

The area of an equilateral triangle inscribed in the circle x²  + y²  – 2x = 0 is

The length of intercept on y-axis, by a circle whose diameter is the line joining the points (–4,3) and (12,–1) is

The gradient of the tangent line at the point (a cos a, a sin a) to the circle x²  + y²  = a² , is

lx + my + n = 0 is a tangent line to the circle x²  + y²  = r² , if

If y = c is a tangent to the circle x² +y² –2x+2y –2 = 0 at (1, 1), then the value of c is

Line 3x + 4y = 25 touches the circle x²  + y²  = 25 at the point

The equations of the tangents drawn from the point (0, 1) to the circle x²  + y²  - 2x + 4y = 0 are

The greatest distance of the point P(10, 7) from the circle x²  + y²  – 4x – 2y – 20 = 0 is

The equation of the normal to the circle x² +y²  = 9 at the point   is

The parametric coordinates of any point on the circle x²  + y²  – 4x – 4y = 0 are

The length of the tangent drawn from the point (2, 3) to the circles 2(x²  + y² ) – 7x + 9y – 11 = 0.

Tangents are drawn from (4, 4) to the circle x²  + y²  – 2x – 2y – 7 = 0 to meet the circle at A and B. The length of the chord AB is

The angle between the two tangents from the origin to the circle (x – 7)²  + (y + 1)²  = 25 equals

Pair of tangents are drawn from every point on the line 3x + 4y = 12 on the circle x² + y²  = 4. Their variable chord of contact always passes through a fixed point whose co-ordinates are

The locus of the mid-points of the chords of the circle x²  + y²  – 2x – 4y – 11 = 0 which subtend 60 ºat the centre is

The locus of the centres of the circles such that the point (2, 3) is the mid point of the chord 5x + 2y = 16 is

The equation of the circle having the lines y²  – 2y + 4x – 2xy = 0 as its normals &passing through the point (2, 1) is

A circle is drawn touching the x-axis and centre at the point which is the reflection of (a, b) in the line y – x = 0. The equation of the circle is

The number of common tangents of the circles x²  + y²  – 2x – 1 = 0 and x²  + y²  – 2y – 7 = 0

The point from which the tangents to the circles x²  + y²  – 8x + 40 = 0,  5x²  + 5y²  – 25 x + 80 = 0, x²  + y²  – 8x + 16y + 160 = 0 are equal in length is

If the circle x²  + y²  = 9 touches the circle x²  + y²  + 6y + c = 0, then c is equal to

The tangent from the point of intersection of the lines 2x – 3y + 1 = 0 and 3x – 2y –1 = 0 to the circle x²  + y²  + 2x – 4y = 0 is

The length of the common chord of circles x²  + y²  – 6x – 16 = 0 and x²  + y²  – 8y – 9 = 0 is

The distance between the chords of contact of tangents to the circle x²  + y²  + 2gx + 2fy + c = 0 from the origin and from the point (g, f) is