    Question

# Let C be the curve(s) given by (ax2+by2+c)(ay2−bx)=0;a,b,c∈R−{0} and a≠b. Then C represents

A
a parabola only if a,b and c are of the same sign.
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B
a circle or a parabola if a and b are of the same sign and c is of opposite sign.
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C
an ellipse or a parabola if a and b are of the same sign and c is of opposite sign.
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D
a hyperbola or a parabola if a and b are of opposite sign
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Solution

## The correct options are A a parabola only if a,b and c are of the same sign. C an ellipse or a parabola if a and b are of the same sign and c is of opposite sign. D a hyperbola or a parabola if a and b are of opposite sign(ax2+by2+c)(ay2−bx)=0 ax2+by2+c=0 or ay2−bx=0 Here ay2−bx=0 represents a parabola ∀ a,b∈R−{0} (i) For ax2+by2+c=0 If a,b,c are of the same sign, then ax2+by2+c=0 is not possible. (∵a,b,c∈R−{0}) So, C will represent parabola only (ii) For ax2+by2=−c, ⇒x2(−c/a)+y2(−c/b)=1 For the above equation to represent an Ellipse, (−ca)>0,(−cb)>0 ⇒(ca)<0,(cb)<0 ⇒ a and b should be of the same sign but c should be of opposite sign. (iii)For ax2+by2=−c to represent hyperbola, (−ca)(−cb)<0 ⇒ab<0 ⇒a and b should be of the opposite sign  Suggest Corrections  0      Similar questions  Explore more