Question
If a circle of radius r is concentric with ellipse 
, then common tangent is inclined to the major axis at an angle-
- None of these
Hint:
find the equations of tangents to the circle and ellipse. apply the condition required to find the value of theta.
The correct answer is:
Equation of tangent to the circle : x cos t + y sin t = r
Equation of tangent to the ellipse :
y= mx + √(a2m2+b2)
for the line to be a tangent to the circle, the perpendicular has to be equal to r
=> √(a2m2+b2)/ √(m2+1) = r
=> a2m2+b2 = m2r2 + r2
m= √(r2-b2)/a2-r2 = tan Ѳ
Ѳ = tan -1(√(r2-b2)/a2-r2 )
the perpendicular distance from the tangent to the center of the circle is equal to the radius of the circle.
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