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Let a and b be non-zero real numbers. Th...

Let a and b be non-zero real numbers. Then the equation : `(ax^2 + by^2 + c)(x^2 - 5xy + 6y^2) = 0` represents :

A

our straight lines. when c= 0 and a=b are of the same sign

B

two straight lines and a circle, where a = b and c is of sign opposite to that of a.

C

two straight lines and a hyperbola when a and b are of the same sign and c is of sign opposite to that of a

D

a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a.

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MODERN PUBLICATION-CONIC SECTIONS-EXERCISE
  1. Consider three points : P (- sin (beta- alpha), - cos beta), Q = (cos...

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  2. Consider two curves C1:y^2=4x ; C2=x^2+y^2-6x+1=0. Then,

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  3. Let a and b be non-zero real numbers. Then the equation : (ax^2 + by^2...

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  4. Consider a branch of the hyperbola : x^2 -2y^2-2sqrt2x-4sqrt2y-6=0 wit...

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  5. Tangents drawn from the piont P(1,8) to the circle x^(2)+y^(2)-6x-4y-1...

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  6. The tangent PT and the normal PN to the parabola y^2=4ax at a point P ...

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  7. The line passing through the extremity A of the major axis and extremi...

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  8. A triangle A B C with fixed base B C , the vertex A moves such that co...

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  9. The normal at a point P, on the ellipse x^2+4y^2=16 meets the x-axis a...

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  10. The locus of the orthocentre of the triangle formed by the lines : (1 ...

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  11. An ellipse intersects the hyperbola 2x^2- 2y^2 = 1 orthogonally. The e...

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  12. The lines p(p^(2)+1)x-y+q=0 and (p^(2)+1)^(2)x+(p^(2)+1)y+2q = 0 are ...

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  13. If P and Q are the points of intersection of the circles x^(2)+y^(2)+3...

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  14. The ellipse x^2+ 4y^2 = 4 is inscribed is a rectangle alligned with th...

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  15. The Line L given by (x)/(5) + (y)/(b) =1 passes through the point (13,...

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  16. The circle x^(2)+y^(2d)=4x+8y+5 intersects the line 3x-4y=m at two dis...

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  17. If two tangents drawn from a point P to the parabola y2 = 4x are at ri...

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  18. Let A and B be two distinct points on the parabola y^2=4x. If the axis...

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  19. A straight line L through the point (3,-2) is incined at an angle 60^...

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  20. The lines x + y =|a| and ax-y= 1 intersect each other in the first qua...

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