the tangent to curv y= x^2 + 6 at a point 1,7 touches the circle x^2+y^2+16x+12y+c=0 at a point q then the coordinates of q are :

ans = -6,-7

The tangent to the curve y=x2+6 at point (1,7) is given by:
x*1+6=12.(y+7)2x+12=y+72x-y+5=0 ............(1)y=2x+5 ...........(2)
if equation (1) is the tangent to the circle x2+y2+16x+12y+c=0
substituting the value of y from eq(2), 
x2+(2x+5)2+16x+12*(2x+5)+c=0x2+4x2+25+20x+16x+24x+60+c=05x2+60x+85+c=0 ..........(3)
since the line (1) touches the given circle, then discriminant of eq(3) must be zero:
thus equation (3) can be rewritten as 5x2+60x+85+95=0
for x=-6 , we have y=2*(-6)+5
if the point of contact is Q, then the coordinates of Q are (-6,-7)

hope this helps you

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