Question

The tangent to the parabola y² = 4x at the point where it intersects the circle x² + y² = 5 in the first quadrant , passes through the point -

(1)   (-1/3, 4/3)

(2)    (3/4, 7/4)

(3)   (1/4, 3/4)

(4)   (-1/4, 1/2)

Answer 1

Correct option  (2)    (3/4, 7/4)

Explanation:

y² = 4x … (i) 

x² + y² = 5 ….(ii) 

for point of intersection x² + 4x – 5 = 0

(x + 5) (x – 1) = 0 

x = – 5 x =1

not possible y = ± 2 

Point in IQ (1, 2)

Tangent at (1, 2) 

2y = 4(x + 1/2)

y = x + 1

point (3/4, 7/4) lies on tangent