Dr. SK Goyal Solutions for Chapter: Circle, Exercise 9: EXERCISE ON LEVEL-II

Author:Dr. SK Goyal

Dr. SK Goyal Mathematics Solutions for Exercise - Dr. SK Goyal Solutions for Chapter: Circle, Exercise 9: EXERCISE ON LEVEL-II

Attempt the practice questions on Chapter 4: Circle, Exercise 9: EXERCISE ON LEVEL-II with hints and solutions to strengthen your understanding. Skills in Mathematics Coordinate Geometry for JEE Main & Advanced solutions are prepared by Experienced Embibe Experts.

Questions from Dr. SK Goyal Solutions for Chapter: Circle, Exercise 9: EXERCISE ON LEVEL-II with Hints & Solutions

HARD
JEE Main/Advanced
IMPORTANT

The line y=mx+am2+1-e2; e2<1, cuts the lines x=±a in T and T'. If Sae,0 and S'-ae,0 are two other points, show that all these four points are con-cyclic.

HARD
JEE Main/Advanced
IMPORTANT

For what values of l and m, circle 5x2+y2+ly-m=0 belongs to the co-axial system determined by the circles
x2+y2+2x+4y-6=0 and 2x2+y2-x=0?

HARD
JEE Main/Advanced
IMPORTANT

'O' is a fixed point and P a point which moves along a fixed straight line not passing through O;Q is taken on OP such that OP·OQ=K (constant). Prove that the locus of Q is a circle. Explain how the locus of Q can still be regarded as as a circle even if the fixed straight line passes through 'Q'.

HARD
JEE Main/Advanced
IMPORTANT

The circles x2+y2+2ax-c2=0 and x2+y2+2bx-c2=0 intersect at A and B. A line through A meets one circle at P and aa parallel line through B meets the other circle at Q. Show that the locus of the mid point of PQ is a circle.

HARD
JEE Main/Advanced
IMPORTANT

A circle of radius 5 meters is having is centre at A at the origin. Two circles II and III with centres at B and C of radii 3 and 4 metres respectively touch the circle I and also touch the x-axis to the right of A. Find the equations to any two common tangents to the circles II and III.

HARD
JEE Main/Advanced
IMPORTANT

If the origin be at one of the limiting points of a system of co-axial circles of which x2+y2+2gx+2fy+c=0 is a member, show that the equation of the system of circles them all orthogonally is
x2+y2g+μf+cx+μy=0.
Also show that other limiting point is -gcg2+f2,-fcg2+f2.

HARD
JEE Main/Advanced
IMPORTANT

The straight line px+qy=1 makes with ax2+2hxy+by2=c, a chord which subtends a right angle at the origin. Show that cp2+q2=a+b. Also show that px+qy=1 touches a circle whose radius is ca+b.

HARD
JEE Main/Advanced
IMPORTANT

A circle of radius 2 units rolls on the outside of the circle x2+y2+4x=0 touching it externally. Find the locus of the centre of this outer circle. Also, find the equations of the common tangents of the two circles when the line joining the centres of the two circles make an angle of 60° with x-axis.