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 :

Answer 1

Answer:

95

Equation of tangent at (1,7) to curve x = y -6 is

x − 1 =  1 2

(y +7) −6

2x - y +5 = 0 ... (i)

Centre of circle = (-8,-6)

Radius of circle = 64 + 36−c = 100−c

∵ Line (i) touches the circle

∴



2(−8) −(−6) +5

4 + 1

= 100−C

5 = 100−c

⇒ c = 95

Answer 2

Answer:

95

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