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Questions  

The tangent to the ellipse 3x2+16y2=12, at the point (1, 3/4), intersects the curve y2+x=0 at :

a
no point
b
exactly one point
c
two distinct points
d
more than two points

detailed solution

Correct option is B

Tangent at 1,34 to the ellipse 3x2+16y2=12 is x⋅14+y3434=1⇒x+4y=4which intersects the curve y2+x=0 at points for whichy2+(4−4y)=0⇒(y−2)2=0⇒y=2  and the points of intersection is (– 4, 2) exactly one point.

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