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The equation 16 x^2+y^2+8x y-74 x-78 y+2...

The equation `16 x^2+y^2+8x y-74 x-78 y+212=0` represents a. a circle b. a parabola c. an ellipse d. a hyperbola

A

a circle

B

a parabola

C

an ellipse

D

a hyperbola

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To determine the type of conic section represented by the equation \( 16x^2 + y^2 + 8xy - 74x - 78y + 212 = 0 \), we can follow these steps: ### Step 1: Identify the coefficients The general form of a conic section is given by: \[ Ax^2 + By^2 + 2Hxy + 2Fx + 2Gy + C = 0 \] From the given equation, we can identify: ...
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RD SHARMA ENGLISH-PARABOLA-All Questions
  1. The coordinates of the focus of the parabola y^2-x-2y+2=0 are a. (5/4...

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  2. The vertex of the parabola (y+a)^2=8a(x-a) is a.(-a ,-a) b. (a ,-a) c....

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  3. If the focus of a parabola is (-2,1) and the directrix has the equatio...

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  4. The equation of the parabola whose vertex is (a ,0) and the directrix ...

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  5. The parametric equations of a parabola are x=t^2+1, y=2t+1. The Cartes...

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  6. vertex and focus of a parabola are (-1,1) and (2,3) respectively. find...

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  7. The locus of the points of trisection of the double ordinates of a ...

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  8. The equation of the directrix of the parabola whose vertex and focus a...

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  9. If V and S are respectively the vertex and focus of the parabola y^2+6...

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  10. The directrix of the parabola x^2-4x-8y + 12=0 is

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  11. The equation of the parabola with focus (0,0) and directrix x+y=4 is a...

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  12. The line 2x−y+4=0 cuts the parabola y^2=8x in P and Q. The mid-point o...

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  13. In the parabola y^2=4a x , the length of the chord pasing through the ...

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  14. The equation 16 x^2+y^2+8x y-74 x-78 y+212=0 represents a. a circle b....

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  15. The length of the latus rectum of the parabola y^2+8x-2y+17=0 is a.2 b...

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  16. The vertex of the parabola (y-2)^2=16(x-1) is a.(1,2) b.(-1,2) c. (1,-...

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  17. The length of latus rectum of the parabola 4y^2+2x−20y+17=0 is (a) 3 (...

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  18. The focus of the parabola y=2x^2+x is a.(0,0) b. (1//2,1//4) c. (-1//2...

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  19. Which of the following points lie on the parabola x^2=4a y ? a.x=a t^...

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  20. The equation of the parabola whose focus is (1,-1) and the directrix i...

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