x = a sec θ + b tan θ
y = a tan θ + b sec θ
x2 + y2 = a2 + b2
x2 + y2 = a2 - b2
x2 - y2 = a2 + b2
x2 - y2 = a2 - b2
x2 = a2sec2θ + b2tan2θ + 2ab secθ tanθ ... (i)
y2 = a2tan2θ + b2sec2θ + 2ab tanθ secθ ... (ii)
Subtracting (ii) from (i), we get
x2 - y2 = a2 - b2 [∵ sec2θ - tan2θ = 1 ]
The locus of the point of intersection of perpendicular tangents to the circles x2+y2=a2 and x2+y2=b2 is
If x=a cosec θ and y=b cot θ, then which of the following equations is true ?
The length of common chord of the circles (x−a)2+y2 =a2 and x2+(y−b)2 = b2 is