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The curve with parametric equations ...

The curve with parametric equations
`x=1 +4cos theta , y= 2 +3 sin theta .` is

A

an ellipse

B

a parabola

C

a hyperbola

D

a circle

Text Solution

Verified by Experts

The correct Answer is:
B
We have ,
`x=1 +4 cos theta , y =2+3 sin theta `
` therefore ((x-1)/(4))^(2)+((y-2)/(3))^(2)=1implies ((x-1)^(2))/(16)+((y-2)^(2))/(9) =1`
Clearly , which is an ellipse .
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OBJECTIVE RD SHARMA-ELLIPSE-Chapter Test
  1. The curve with parametric equations x=1 +4cos theta , y= 2 +3 s...

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  2. Find the maximum area of an isosceles triangle inscribed in the ellip...

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  3. A tangent to the ellipse x^2+4y^2=4 meets the ellipse x^2+2y^2=6 at P&...

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  4. If the distance of a point on the ellipse (x^(2))/(6) + (y^(2))/(2) = ...

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  5. If the minor axis of an ellipse subtends an angle of 60^(@) at each fo...

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  6. Let Sa n dS ' be two foci of the ellipse (x^2)/(a^3)+(y^2)/(b^2)=1 . I...

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  7. The equation of the normal at the point P (2, 3) on the ellipse 9x^(2)...

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  8. For the ellipse 3x^(2) + 4y^(2) + 6x - 8y - 5 = 0 the eccentrically, i...

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  9. Let S, S' be the focil and BB' be the minor axis of the ellipse (x^(2)...

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  10. If the length of the latusrectum of the ellipse x^(2) tan^(2) theta + ...

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  11. if vertices of an ellipse are (-4,1),(6,1) and x-2y=2 is focal chord t...

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  12. If (-4, 3) and (8, 3) are the vertices of an ellipse whose eccentricit...

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  13. The area of the triangle formed by three points on the ellipse x^2/a^2...

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  14. If the chord joining points P(alpha)a n dQ(beta) on the ellipse ((x...

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  15. If P(alpha,beta) is appoint on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=...

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  16. The tangent at any point P on the ellipse meets the tangents at the ve...

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  17. P is a point on the circle x^(2) + y^(2) = c^(2). The locus of the mid...

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  18. The locus of the poles of normal chords of the ellipse x^(2)/a^(2) + y...

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  19. The locus of mid-points of a focal chord of the ellipse x^2/a^2+y^2/b^...

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  20. The locus of points whose polars with respect to the ellipse x^(2)/a^(...

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  21. if the chord of contact of tangents from a point P to the hyperbola x...

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