Equation of Tangent at a Point (x,y) in Terms of f'(x)
The equation ...
Question
The equation of the tangents to 4x2−9y2=36 which are perpendicular to the straight line 2y+5x=10 are
A
5(y−3)=2(x−√1174)
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B
5(y−2)=2(x−√−18)
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C
5(y+2)=2(x−√−18)
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D
none of these
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Solution
The correct option is D none of these Given, 2y+5x=10 2y′+5=0 y′=−52. Hence the required slope is 25. Now 4x2−9y2=36. 4x2−36=9y2 y=13.√4x2−36. y′=8x6√4x2−36=25 40x=12√4x2−36 10x=3√4x2−36 100x2=36x2−324 64x2=−324 x2=−8116. Hence no real values of x. Hence answer is none of these.