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Question

The tangent to the curve x2+y2=25 parallel to the line 3x-4y=7 exist at the point


A

(-3, -4)

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B

(3, -4)

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C

(3, 4)

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D

(1,1)

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Solution

The correct option is B

(3, -4)


We have,
x2+y2=252x+2ydydx=0dydx=xy.
Now, slope of the line 3x -4y =7 is m =34.
Since the tan gent is parallel to the given line.
dydx=34xy=34y=43x.
From equation (1): x2+169x2=25x=±3.
If x =3, from equation (2), y=43(3)=4.
If x =-3, from equation (2), y=43(3)=4.
The point s are (3,-4) and (-3, 4).
Hence (b) is the correct answer.


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