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Q) the tangent drawn to the parabola y= x.x + 6 at the point (1,7) touches the circle x.x + y.y +16x +12y + c = 0 at the point: (a) (-6,-7) (b) (-10,-15) (c) (-9,-7) (d) (13,7)

Q) the tangent drawn to the parabola y= x.x + 6 at the point (1,7) touches the circle x.x + y.y +16x +12y + c = 0 at the point: 


(a) (-6,-7)


(b) (-10,-15)


(c)  (-9,-7)


(d) (13,7)

Grade:Upto college level

1 Answers

vikas askiitian expert
509 Points
11 years ago

y = x2+6

dy/dx = slope = m = 2x

                        m=2             ( at point (1,7) )

eq of tangent at 1,7  : y-7 = (x-1)2

                        2x-y+5 = 0             ......................1

x2+y2+16x+12y+c = 0

now we have to make a tanget at point (x1,y1) which lies on circle

replace x2 by xx1 , y2 by yy1 & x by x+x1/2 , y by y+y1/2

eq of tangent = x(x1+8) + y(y1+6) + 8x1+6y1+c = 0    .....................2

eq of line 1 touches the circle so eq1 & 2 are equivalent so

ratios of cofficient of x,y is constant

x1+8/2 = y1+6/-1

 x1+2y1+20 = 0            ................3

(x1,y1) will satisfy eq 1 so

 2x1-y1+5=0          .....................4

solving 3 & 4 we get

(x1,y1) = (-6,-7)

 

approve my ans if u like it

 

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