Find the points in which the line y = 2x + 1 cuts the circle `x^(2) + y^(2) = 2`.

Find the range of values of m for which the line y=m x+2 cuts the circle x^2+y^2=1 at distinct or coincident points.

If centre of a circle lies on the line 2x - 6y + 9 =0 and it cuts the circle x^(2) + y^(2) = 2 orthogonally then the circle passes through two fixed points

Find the co-ordinates of the point of intersection of tangents at the points where the line 2x + y + 12 = 0 meets the circle x^2 + y^2 - 4x + 3y - 1 = 0

The locus of centres of all circles which touch the line x = 2a and cut the circle x^2 + y^2 = a^2 orthogonally is

For all values of m in R the line y - mx + m - 1 = 0 cuts the circle x^2 + y^2 - 2x - 2y + 1 = 0 at an angle

A circle touching the line x +y - 2 = 0 at (1,1) and cuts the circle x^(2) +y^(2) +4x +5y - 6 = 0 at P and Q. Then

Prove that the straight line y = x + a sqrt(2) touches the circle x^(2) + y^(2) - a^(2)=0 Find the point of contact.

Find the number of points at which line 6y + 4x = 5 cuts hyperbola ((x - 1)^(2))/9 - ((y - 2)^(2))/4 = 1 .

At how many points does the line y=2x-1 intersect the circle (x-4)^(2)+(y-6)^(2)=2 ?

Find the condition for the line y=m x to cut at right angles the conic a x^2+2h x y+b y^2=1.