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Question

If θ is the acute angle of intersection at a real point of the circle x2+y2=5 and the parabola y2=4x, then tanθ is equal to

A
1
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B
3
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C
3
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D
13
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Solution

The correct option is C 3
Given equations are
x2+y2=5.....(i)
and y2=4x.....(ii)
On solving Eqs. (i) and (ii), we get
x=5,1
at x=5,y2=20 (imaginary value)
at x=1,y2=4
y=±2
Hence, point of intersection are (1,2) and (1,2)
On differentiating Eq. (i) w.r.t. x, we get
2x+2ydydx=0
dydx=xy
m1=(dydx)(1,2)=12
And on differentiating Eq. (ii) w.r.t. x, we get
2ydydx=4
dydx=2y,m2=(dydx)(1,2)=22=1
Now, tanθ=m1m21+m1m2
=∣ ∣ ∣121112∣ ∣ ∣=∣ ∣ ∣3212∣ ∣ ∣=3

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