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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 coordinates of its vertex, the equation of its latus rectum

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CENGAGE PUBLICATION-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 centre of a circle, which intercepts a cho...

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  6. Find the value of lamda if the equation 9x^(2)+4y^(2)+2lamdaxy+4x-2y+3...

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

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

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  9. LOL' and MOM' are two chord of parabola y^(2)=4ax with vertex A passin...

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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 normal drawn from a point to the parabola ...

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  12. If three distinct normals to the parabola y^(2)-2y=4x-9 meet at point ...

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  13. Find the locus of the point of intersection of two normals to a parabo...

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  14. P(t(1))andQ(t(2)) are points t(1)andt(2) on the parabola y^(2)=4ax. ...

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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=ax^(2)+bx+c ...

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  18. If a focal chord of y^(2)=4ax makes an angle alphain[pi//4,pi//2] with...

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

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

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