Download PTU B.Sc CS-IT 2020 March 2nd Sem 71507 Coordinate Geometry Question Paper

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Roll No. [ | [ [T TTT] Total No. of Pages : 02
Total No. of Questions : 07

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have to attempt any FOUR questions.

SECTION-A

1. Answer briefly :
   1. Define an ellipse and a parabola.

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   2. Find the equation of the ellipse having major axis along x-axis and minor axis along y-axis, eccentricity > and the distance between the foci as 4.
   3. Find the equation to the two straight lines through the origin perpendicular to the lines 5x² — 7xy — 3y² =0.
   4. Find the points of the parabola y² = 8x, whose ordinate is twice the abscissa.
   5. State and prove the reciprocal property of pole and polar with respect to a parabola.
   6. Find the equation to the circle which passes through the points (1, 0), (0, —6) and (3, 4).

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   7. Find the equation of normal to a parabola in the slope form.
   8. Find the equation of the hyperbola whose asymptotes are the lines x + 2y + 1 =0 and 2x +y + 3 =0 and which passes through the point (1, 2)
   9. Find the transformed equation of 17x²-16xy + 17y²-225 = 0 when the axes are rotated through an angle of 45°.
   10. Find the equations of the straight lines bisecting the angles between the pair of straight lines 4x²— 16xy + 7y² =0

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SECTION-B

2. a) On shifting the origin to the point (1, —1) the axes remaining parallel to the original axis, the equation of a curve becomes 4x² + y² + 3x — 4y + 2 = 0. Find its original equation.
   b) Find the value of A for which the equation 12x² — 10xy + 2y² + 11x = 5y + A = 0 represents a pair of straight lines. Also find the angle between them.
3. a) Find the equation of tangent to the circle x² + y² = a² which is parallel to the straight line y =mx + c.
   

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   b) Define polar of a point. Find the polar of the point (1, 2) with respect to the circle x² +y² =7
4. a) Define orthogonal circles. Prove that the pair of circles x² + y² —2ax + c =0 x² +y² + 2by — c = 0 intersect orthogonally.
   b) Show that the lines joining the origin to the points of intersection of x²+y²+2gx+c=0 and x²+y²+2fy—c=0 are at right angles if g²—f²=2c.
5. a) Find the equation of chord of the parabola y² = 4ax in terms of its middle point (x₁, y₁)
   b) Define a parabola. If chords of the parabola y² = 4ax are drawn at fixed distance ‘a’ from the focus, show that the [locus of their poles w.r.t. the parabola is y² =4a(2a + x).

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6. a) Show that the line x + 2y -4 = 0 touches the ellipse 3x² + 4y² = 12. Also find the point of contact.
   b) Prove that the locus of the middle points of normal chords of the rectangular hyperbola x² — y² =a² is (y² — x²)³ = 4a⁴x²y².
7. a) Define a conjugate hyperbola. Prove that if a pair of diameters be conjugate w.r.t. a hyperbola then they will also be conjugate w.r.t. the conjugate hyperbola.
   b) Find the eccentricity, the foci and directrices of the ellipse 3x²+ 4y²— 12x—8y +4=0.

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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