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Prove that the equation of the parabola ...

Prove that the equation of the parabola whose focus is (0, 0) and tangent at the vertex is `x-y+1 = 0 ` is `x^2 + y^2 + 2xy - 4x + 4y - 4=0`.

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ARIHANT MATHS-PARABOLA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Prove that the equation of the parabola whose focus is (0, 0) and tang...

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  2. Let A and B be two finite sets such that n(A) =85, n(B) = 65and n(A ∪ ...

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  3. Let P be the point (1,0) and Q be a point on the locus y^(2)=8x. The l...

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  4. The axis of a parabola is along the line y=x and the distance of its v...

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  5. In a school, all pupils play either Hockey or Football or both. 400 pl...

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  6. The locus of the vertex of the family of parabolas y=(a^3x^2)/3+(a^(2x...

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  7. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

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  8. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  9. Consider the circle x^2 + y^2 = 9 and the parabola y^2 = 8x. They inte...

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  10. Find slope of tangent to the curve if equation is x^2 + y^2 = 9

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  11. Statement 1 : The curve y=-(x^2)/2+x+1 is symmetric with respect to th...

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  12. The equation of a tangent to the parabola y^2=""8x""i s""y""=""x""+"...

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

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  14. If a parabola has the origin as its focus and the line x = 2 as the ...

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  15. In a school, there are 30 teachers who teach Mathematics or Physics. O...

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

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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. Of the 125 students in an elementary school, 89 students play checkers...

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  19. What is the 5th term of this sequence 9, 13, 17, ...?

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  20. In a group of 400 people, 250 can speak Punjabi and 200 can speak Engl...

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  21. If f (x) = a cos (bx + c) + d, then what is the range of f (x)?

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