Question

PLEASE TELL ME THE ANSWER
Find the equations of the tangents to the circle x2 + y2 = 25 which are parallel to the line
y = 2x + 4.​

Answer 1

EXPLANATION.

Equation of tangent to the circle

→ x² + y² = 25.

Parallel to the line y = 2x + 4.

Radius of the circle = 5.

→ 2x - y + 4 = 0.

Equation of tangent parallel to the line

2x - y + 4 = 0 are 2x - y + K = 0.

$\sf \: \implies \: r \: = | \dfrac{ax + by + c}{ \sqrt{ {a}^{2} + {b}^{2} } } | \\ \\ \sf \: \implies \: 5 = | \frac{2x - y + k}{ \sqrt{ {a}^{2} + {b}^{2} } } | \\ \\ \sf \: \implies \: 5 = | \frac{2(0) - 0 + k}{ \sqrt{4 + 1} } | \\ \\ \sf \: \implies \: 5 = | \frac{k}{ \sqrt{5} } | = k \: = 5 \sqrt{5}$

Equation of tangent = 2x - y + 5√5 = 0