Conic Sections ...

If the line 2x –y + λ = 0 is a diameter of the circle  x² +y² +6x −6y+5 = 0 then  λ=

Length of common chord of the circles  x² +y² +2x+6y = 0 and  x² +y² −4x −2y −6 = 0 is  

The circles  x² +y² +6x+6y = 0 and  x² +y² −12x −12y = 0

The equation  x² +y²  = 0 represents

The equation 3  (x² +y² )+5x −7y −2 = 0 represents

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

If  (x² −a)² +(y −b)²  = c²  represents a circle, then

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

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

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

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

The equation  ax² +by² +2hxy+2gx+2fy+c = 0 represents a circle only if

x² +y² −6x+8y −11 = 0 is a circle. The points (0, 0) and (1, 8) lie

The length of tangent from the point (2, - 3) to the circle  2x² +2y²  = 1 is

Which one of the following lines is farthest from the centre of the circle  x² +y²  = 10?

Which of the following lines is a normal to the circle  (x −1)² +(y −2)²  = 10

A circle with its centre on the line y = x + 1 is drawn to pass through the origin and touch the line y = x + 2. The centre of the circle is

Four distinct points  (2 λ,3 λ),(1,0),(0,1) and (0, 0) lie on a circle for

The locus of the point of intersection of the lines x cos  α + y sin  α= a  and x sin  α - y cos  α = b is

The line y = m x + c is a normal to the circle  x² +y² +2gx+2fy+c = 0 if

The line 3x –4y = 0

The equations x = a cos θ + b sin  θ , and  y = a sin θ−b cos θy = a sin ⁡θ−b cos ⁡θ , 0  ≤ θ≤2  π represent

The number of points which have the same power w.r.t. two (different) concentric circles is

A circle passes through (0, 0) ( a, 0), (0, b). The coordinates of its centre are

The focus of the parabola  x² −8x+2y+7 = 0 is