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Question

Assertion :The conic xa+yb=1 represents a parabola, where a,b0. Reason: The second degree equation Ax2+2Hxy+By2+2Gx+2Fy+c=0 represents a parabola if Δ0 & H2=AB.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
xa+yb=1
On squaring both sides we get xa+yb+2xyab=1 xa+yb1=2xyab
Again squaring both sides, we get x2a2+y2b2+1+2xyab2xa2yb=4xyab
x2a22xyab+y2b22xa2yb+1=0
Now comparing with the equation given in Reason (R) A=1a2,B=1b2,H=1ab,G=1a,F=1b,C=1
Δ=ABC+2FGHAF2BG2CH2
=1a2b22a2b21a2b21a2b21a2b2=4a2b20 as a0,b0 & H2=AB
Δ0,H2=AB Conic is a parabola

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