Question

If the tangent at (1, 7) to the curve x² = y – 6 touches the circle x² + y² + 16x + 12y + c = 0 then the value of c is ______.

पर्याय

• 185

• 85

• 95

• 195

Answer 1

If the tangent at (1, 7) to the curve x² = y – 6 touches the circle x² + y² + 16x + 12y + c = 0 then the value of c is 95.

Explanation:

Equation of tangent at (1, 7) to x² = y – 6 is 2x – y + 5 = 0.

Now, perpendicular from centre O(–8, –6) to 2x – y + 5 = 0 should be equal to radius of the circle

∴ `|(-16 + 6 + 5)/sqrt(5)| = sqrt(64 + 36 - C)`

`\implies sqrt(5) = sqrt(100 - c)`

`\implies` c = 95