Solutions of Equation of Circle for SEE Exam

Solutions of Equation of Circle for SEE Exam


Q. no. 1. The sides of a rectangle are x=2, x= -1, y=5 and y=2. Find the equation of the circle circumscribing the rectangle.



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2. P is the center of the circle x²+y²-4x-10y+4=0 and the equation of its chord AB is x-y+2=0. If C is the mid-point of AB, find the equation of PC.







3. Show that the circles x
²+y²=100 and x²+y²-24x-10y+160=0 touch externally.







4. Show that the circles x
²+y²+2x-6y+9=0 and x²+y²+8x-6y+9=0 touch internally.







5. If the circles x
²+y²+2ax+c²=0 and x²+y²+2by+c²=0 touch externally, prove that 1/a²+1/b²=1/c².







6. Find the equation of a circle passing through the point (4,-2) touching the both axes and completely lies in the fourth quadrant.









7. If y=2x is a chord of the circle x²+y²-10x=0, find the equation of the circle with this chord as the diameter.







8. Find the equation of the diameter of the circle x²+y²-4x-6y-12=0 which passes through the origin.





9. Test whether the points (1,2), (-3,1) and (0, √2) are outside or inside or on the circle x²+y²+4x-2=0.



















10. Find the equation of a circle of radius 5 units which lies within a circle x²+y²+14x+10y-26=0 and which touches it at the point (-1,3).








11. Find the equation of tangents drawn from (4,3) to the circle x²+y²=4.








12. the equation of a circle with center (2,3) and touches a straight line 4x+3y-2=0 at a point.




13. Find the equation of the circle whose center is (4,5) and touches the line 3x+4y-2=0.


14. Show that the line 3x+y+7√10=0  touches the circle x²+y²-2x+6y-39=0.






15. If the line 4x+3y+k=0 touches the circle x²+y²-4x+10y+4=0, find the value of k.














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6. If the line ax+by+c=0 touches the circle x²+y² +2gx+2fy+c=0, prove that (g²+f²-c) (a²-b²)= (c-ag-bf)².




17. Find the equation of a line which touches the circle x²+y²=9 and which is parallel to the line 3x+4y=3.





18. Find the equation of a line which touches the circle x²+y²=25 and which is perpendicular to the
line 12x-5y-7=0.






19. Find the equation of the line which touches the circle x²+y²-14x-4y-5=0 at the point (10,y).








20. Find the length of the either tangent drawn from the point (4,5) to the circle x²+y²-4y-5=0.





  21. Find the equation of the tangent to the circle x²+y²=25 at the point (3,-4).






 22. Find the equation of the circle concentric with the circle x²+y²-2x-10y+1=0 and passing through the point (2,-3).





23. Find the equation of the circle whose center is (4,4) and touches both axes.



24. Define parabola and give the example in figure.

25. Mention the condition of generating a hyperbola by the intersection of a plane surface and a cone.
26. What is the name of angle α in the given figure?


27. Write the condition of generating an ellipse by the intersection of a cone and a plane surface.


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