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

Engineering

Mathematics

Tangent and Normal

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

$(- \frac{1}{3}, \frac{4}{3})$

$(- \frac{1}{4}, \frac{1}{2})$

$(\frac{3}{4}, \frac{7}{4})$

$(\frac{1}{4}, \frac{3}{4})$

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x² + 4x = 5

⇒ x = – 5, x = 1

⇒ P (1, 2)

Tangent at P is y = x + 1

$(\frac{3}{4}, \frac{7}{4}) lies on this .$