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Practical Session No. 6

 Circle and parabola

1) Find the center and radius of the circle 𝑥𝑥2+𝑦𝑦2−𝑥𝑥+2𝑦𝑦−3=0

2) Find the equation of circle passing through the point of intersection of the lines

𝑥𝑥+3𝑦𝑦=0 and 2𝑥𝑥−7𝑦𝑦=0 and whose centre is the point of intersection of the lines 𝑥𝑥+𝑦𝑦+1=0 and 𝑥𝑥−2𝑦𝑦+4=0.

3) Find the equation of circle, the end points of whose diameter are the centers of circles

𝑥𝑥2+𝑦𝑦2+6𝑥𝑥−14𝑦𝑦−1=0 and 𝑥𝑥2+𝑦𝑦2−4𝑥𝑥+10𝑦𝑦−2=0.

4) Find the equation of the circle passing through points (5,7),(6,6) and (2,−2).

5) Consider a circle with center at origin and radius r. Let P(x, y) be any point on the circle making an angle θ with positive direction of the X - axis then verify that

P(x, y) = P (r cosθ , r sinθ ). By taking r = 5 and θ = 1350 verify the above result.

6) Find the equations of tangents to the circle 𝑥𝑥2+𝑦𝑦2=4 drawn from the point (2, −1).

7) Find the co-ordinates of the focus, equation of the directrix, length of Latus Rectum, and the co-ordinates of the end points of the Latus Rectum of the parabola

𝑖) 5 𝑦𝑦2=24𝑥𝑥 , 𝑖 ) 𝑥𝑥2=12 𝑦𝑦 , 𝑖 𝑖 ) 3 𝑦𝑦2=−16 𝑥𝑥 .

8) Find the co-ordinates of the focus, equation of the directrix, length of Latus Rectum, and the co-ordinates of the end points of the Latus Rectum of the parabola 𝑥𝑥2+4𝑥𝑥+4𝑦𝑦+16=0.

9) Find the area of triangle formed by the lines joining the vertex of the parabola 𝑥𝑥2=12𝑦𝑦 to the ends of its Latus rectum.

10) For which point of the parabola 𝑦𝑦2=18𝑥𝑥 is the ordinate equal to 3 time the abscissa?

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