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Trignometry

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20 Nov 2011 22:43:22 IST

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tangent to the curve y=x^2+6 at a point (1,7) touches the circle x^2+y^2+16x+12y+c=0 at Q.

Mathematics

tangent to the curve y=x^2+6 at a point (1,7) touches the circle x^2+y^2+16x+12y+c=0 at Q.

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Arjun Virmani

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Joined: 1 Jun 2009

Posts: 1294

20 Jan 2012 16:06:47 IST

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To write the eq of tangent for any 2 degree curve at any point (h,k) on the curve, just replace x^2 and y^2 by hx and ky respectively and all the x and y from (x+h)/2 and (y+k)/2 resp..............

Its a direct trick and can be proven!!!

doing the same!!

tangent to the given curve.

y=x^2+6 is (y+k)/2 = hx + 6

substitute the point given (1,7)

y + 7 = 2 (x + 6)

now this line is tangent to the circle at (a,b) (let)

equate the slope and put the point in the eq. of circle.

u'll get co-ordinates (a,b) in terms of c!!!!

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