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Question

The number of values of c such that the straight line y=4x+c touches the curve x24+y2=1 is

A
0
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B
1
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C
2
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D
infinite
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Solution

The correct option is C 2
We know that the line y=mx+c touches the curve x2a2+y2b2=1 if c2=a2m2+b2
Here a2=4,b2=1,m=4
c2=64+1c=±65

c=+65 and65

c has 2 values

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