Manipal MET2013MathematicsEllipse
If the tangent to ellipse x^2+2 y=1 at point P ( 1 2 , 1 2 ) meets the auxiliary circle at the points R and Q , then tangents to circle at Q and R intersect at
Options
- A( 1 2 , 1 )
- B(1, 1 2 )
- C( 1 2 , 1 2 )
- D( 1 2 , 1 2 )
Correct answer
A. ( 1 2 , 1 )
Step-by-step solution
Equation of tangent to ellipse at given point is x ( 1 2 )+2 y ( 1 2 )=1 . x+ 2 y= 2 ....(i) Now, Q R is chord of contact of circle x^2+y^2=1 with respect to point T(h, K) . then, Q R h x+K y=1 ....(ii) Equations (i) and (ii) represent same straight line, then comparing ratio of coefficients we have h 1 = K 2 = 1 2 Hence; (h, K) ( 1 2 , 1 )