Differentiating x2=y−6 with respect to x,
2x=dxdy
dxdy∣(1,7)=2×1=2
Hence, equation of tangent is y−7=2(x−1)
⇒y=2x+5
Distance from centre =
[12+22−6−2(−8)−5]
⇒∣55∣=5
Radius of circle =82+62−c
⇒100−c=5
⇒c=95
If the tangent at (1,7) to the curve x2=y−6 touch the circle x2+y2+16x+12y+c=0 then the value of c is:
Held on 8 Apr 2018 · Verified 6 Jul 2026.
95
195
185
85
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