Find the point on the hyperbola x2−9y2=9 where the line 5x+12y=9 touches it.
If from any point P on the circle x2+y2+2gx+2fy+c=0, tangents are drawn to the circle x2+y2+2gx+2fy+csin2α+(g2+f2)cos2α=0 , then find the angle between the tangents.
Find the area of the triangle formed by the tangents from the point (4, 3) to the circle x2+y2=9 and the line joining their points of contact.
Find the length of the tangent drawn from any point on the circle x2+y2+2gx+2fy+c1=0 to the circle x2+y2+2gx+2fy+c2=0
Find the equation of the circle with radius 5 whose center lies on the x-axis and passes through the point (2, 3).
Find the equation of the circle passing through the origin and cutting intercepts of lengths 3 units and 4 unitss from the positive exes.
Two circles with radii aandb touch each other externally such that θ is the angle between the direct common tangents, (a>b≥2) . Then prove that θ=2sin−1(a+ba−b) .