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Find the value of lambda if the equation...

Find the value of `lambda` if the equation `(x-1)^2+(y-2)^2=lambda(x+y+3)^2` represents a parabola. Also, find its focus, the equation of its directrix, the equation of its axis, the coordinates of its vertex, the equation of its latus rectum, the length of the latus rectum, and the extremities of the latus rectum.

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CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Find the equation of parabola having focus at (1,1) and vertex at (-3,...

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  2. Find the equation of the parabola with focus f(4,0) and directrix x=−4...

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  3. Find the value of lambda if the equation (x-1)^2+(y-2)^2=lambda(x+y+3)...

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  4. The equation of the latus rectum of a parabola is x+y=8 and the equati...

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  5. Prove that the locus of the center of a circle, which intercepts a cho...

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  6. Find the value of lambda if the equation 9x^2+4y^2+2lambdax y+4x-2y+3=...

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  7. Find the range of values of lambda for which the point (lambda,-1) is ...

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  8. Prove that the locus of a point, which moves so that its distance from...

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  9. L O L ' and M O M ' are two chords of parabola y^2=4a x with vertex A ...

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  10. If (a ,b) is the midpoint of a chord passing through the vertex of the...

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  11. If two of the three feet of normals drawn from a point to the parabola...

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  12. If three distinct normals can be drawn to the parabola y^2-2y=4x-9 fro...

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  13. Find the locus of thepoint of intersection of two normals to a parabol...

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  14. P(t1) and Q(t2) are the point t1a n dt2 on the parabola y^2=4a x . The...

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  15. Prove that the locus of the point of intersection of the normals at th...

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  16. Find the number of distinct normals that can be drawn from (-2,1) to t...

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  17. If the line passing through the focus S of the parabola y=a x^2+b x+c ...

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  18. If a focal chord of y^2=4a x makes an angle alpha in [0,pi/4] with the...

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  19. Find the length of the normal chord which subtends an angle of 90^@ at...

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  20. Find the locus of the point of intersection of the normals at the end ...

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