Chapter 3: Analytical Geometry March 14, 2024 Maven Leave a Comment Welcome to the Chapter 3: Analytical Geometry Name Email 1. If the centre of the circle is (–a, –b) and radius is $\sqrt{a^{2}-b^{2}}$, then the equation of circle is $x^{2}+y^{2}+2ax+2by+2b^{2}=0$ $x^{2}+y^{2}+2ax+2by-2b^{2}=0$ $x^{2}+y^{2}-2ax-2by-2b^{2}=0$ $x^{2}+y^{2}-2ax-2by+2b^{2}=0$ None 2. Combined equation of co-ordinate axes is $x^{2}-y^{2}=0$ $x^{2}+y^{2}=0$ xy=c xy=0 None 3. The equation of the circle with centre (3, –4) and touches the x – axis is $(x-3)^{2}+(y-4)^{2}=4$ $(x-3)^{2}+(y+4)^{2}=16$ $(x-3)^{2}+(y-4)^{2}=16$ $x^{2}+y^{2}=16$ None 4. In the equation of the circle $x^{2}+y^{2}=16$, y intercept is (are) 4 16 $\pm 4$ $\pm 16$ None 5. The equation of the circle with centre on the x axis and passing through the origin is $x^{2} -2ax+ y^{2}=0$ $y^{2} -2ay+ x^{2}=0$ $x^{2} + y^{2}=a^{2}$ $x^{2} -2ay+ y^{2}=0$ None 6. The centre of the circle $x^{2} + y^{2}-2x+2y-9 =0$ is (1 ,1) (–1, –1) (–1,1) (1, –1) None 7. If the perimeter of the circle is 8$\pi$ units and centre is (2,2) then the equation of the circle is $(x-2)^{2}+(y-2)^{2}=4$ $(x-2)^{2}+(y-2)^{2}=16$ $(x-4)^{2}+(y-4)^{2}=2$ $x^{2}+y^{2}=4$ None 8. $ax^{2}+4xy+2y^{2}=0$ represents a pair of parallel lines then ‘a’ is 2 -2 4 -4 None 9. The focus of the parabola $x^{2} =16y$ is (4 ,0) (–4 , 0) (0, 4) (0, –4) None 10. Length of the latus rectum of the parabola $y^{2}=-25x$ 25 -5 5 -25 None 11. If the lines 2x - 3y - 5 = 0 and 3x - 4y - 7 = 0 are the diameters of a circle, then its centre is ( –1, 1) (1,1) (1, –1) (–1, –1) None 12. The locus of the point P which moves such that P is always at equidistance from the line x + 2y + 7 = 0 is x + 2y + 2 = 0 x - 2y + 1 = 0 2x - y + 2 = 0 3x + y + 1 = 0 None 13. The slope of the line 7x + 5y - 8 = 0 is $\frac{7}{5}$ -$\frac{7}{5}$ $\frac{5}{7}$ -$\frac{5}{7}$ None 14. The length of the tangent from (4,5) to the circle $x^{2} + y^{2} =16$ is 4 5 16 25 None 15. If $m_{1}$ and $m_{2}$ are the slopes of the pair of lines given by $ax^{2}+ 2hxy + by^{2}= 0$, then the value of $m_{1}+ m_{2}$ is $\frac{2h}{b}$ -$\frac{2h}{b}$ $\frac{2h}{a}$ -$\frac{2h}{a}$ None 16. (1, –2) is the centre of the circle $x^{2} + y^{2} + ax + by - 4=0$, then its radius is 3 2 4 1 None 17. The locus of the point P which moves such that P is at equidistance from their coordinate axes is y=$\frac{1}{x}$ y =$- x$ y = $x$ y=$-1\frac{1}{x}$ None 18. The angle between the pair of straight lines $x^{2}-7xy+4y^{2}=0$ is $tan^{-1}\frac{1}{3}$ $tan^{-1}\frac{1}{2}$ $tan^{-1}\frac{\sqrt{33}}{5}$ $tan^{-1}\frac{5}{\sqrt{33}}$ None 19. If $kx^{2} + 3xy - 2y^{2} = 0$ represent a pair of lines which are perpendicular then k is equal to $\frac{1}{2}$ $-\frac{1}{2}$ 2 -2 None 20. The x–intercept of the straight line 3x + 2y - 1 = 0 is 3 $\frac{1}{3}$ $\frac{1}{2}$ None 21. The eccentricity of the parabola is 3 2 0 1 None 22. The double ordinate passing through the focus is focal chord latus rectum directrix axis None 23. The distance between directrix and focus of a parabola $y^{2}=4ax$ is a 2a 4a 3a None 24. If the circle touches x axis, y axis and the line x = 6 then the length of the diameter of the circle is 6 3 12 4 None 25. The equation of directrix of the parabola $y^{2}=-x$ is 4x + 1 = 0 4x - 1 = 0 x - 4 = 0 x + 4 = 0 None Time's up Related Posts:Chapter 1: Introduction to Micro EconomicsChapter 2. Consumption AnalysisChapter 3: Production AnalysisChapter 4: Cost and Revenue Analysis
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