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If a pair of variable straight lines `x^2 + 4y^2+alpha xy =0` (where `alpha` is a real parameter) cut the ellipse `x^2+4y^2= 4` at two points A and B, then the locus of the point of intersection of tangents at A and B is

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. A point on the ellipse x^2+3y^2=37 where the normal is parallel to the...

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  2. Let P(a sectheta, btantheta) and Q(aseccphi , btanphi) (where theta+...

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  3. If a pair of variable straight lines x^2 + 4y^2+alpha xy =0 (where alp...

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  4. The line 2x + y = 1 is tangent to the hyperbola x^2/a^2-y^2/b^2=1. I...

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  5. The equation 3x^2+4y^2-18+16 y+43=k represents an empty set, if k<0 ...

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  6. Which of the following is/are true about the ellipse x^2+4y^2-2x-16 y+...

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  7. If a ray of light incident along the line 3x+(5-4sqrt(2))y=15 gets ref...

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  8. If the sum of the slopes of the normal from a point P to the hyperbol...

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  9. If the tangent at the point P(theta) to the ellipse 16 x^2+11 y^2=256 ...

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  10. If the normal to the given hyperbola at the point (c t , c/t) meets th...

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  11. If the equation of the ellipse is 3x^2+2y^2+6x-8y+5=0 , then which o...

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  12. A normal to the hyperbola (x^2)/4-(y^2)/1=1 has equal intercepts on th...

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  13. If the chord through the points whose eccentric angles are theta and v...

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  14. The number of points on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=3 from w...

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  15. The coordinates (2, 3) and (1, 5) are the foci of an ellipse which ...

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  16. If tangents P Qa n dP R are drawn from a variable point P to thehyperb...

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  17. If the variable line y=k x+2h is tangent to an ellipse 2x^2+3y^2=6, th...

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  18. The locus of a point, from where the tangents to the rectangular hyp...

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  19. The value of a for the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), if t...

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  20. The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 me...

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