Exercise-4

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Embibe Experts Mathematics Solutions for Exercise-4

Simple step-by-step solutions to Exercise-4 questions of Circle from Alpha Question Bank for Engineering: Mathematics. Also get 3D topic explainers, cheat sheets, and unlimited doubts solving on EMBIBE.

Questions from Exercise-4 with Hints & Solutions

HARD
JEE Main/Advance
IMPORTANT

Pa, b is a point in the first quadrant. If the two circles which pass through P and touch both the co-ordinate axes cut at right angles, then find the condition in a and b.

MEDIUM
JEE Main/Advance
IMPORTANT

Show that if one of the circle x2+y2+2gx+c=0 and x2+y2+2g1x+c=0 lies within the other, then gg1 and C are both positive.

HARD
JEE Main/Advance
IMPORTANT

Let ABCD is a rectangle. The incircle of ABD touches BD at E. Incircle of ΔCBD toches BD at F. If AB=8 units, and BC=6 units, then find the length of EF.

HARD
JEE Main/Advance
IMPORTANT

Let circles S1 and S2 of radii r1 and r2 respectively r1>r2 touches each other externally. Circle S of radius r touches S1 and S2 externally and also their direct common tangent. Prove that the triangle formed by joining centre of S1, S2 and S is obtuse angled triangle.

HARD
JEE Main/Advance
IMPORTANT

Circles are drawn passing through the origin O to intersect the coordinate axes at points P & Q such that m·OP+n·OQ is a constant. Show that the circles pass through a fixed point

MEDIUM
JEE Main/Advance
IMPORTANT

The curves whose equations are
S=ax2+2hxy+by2+2gx+2fy+c=0 

S'=a'x2+2h'xy+b'y2+2g'x+2f'y+c'=0  intersect in four concyclic points then find relation in a, b, h, a', b', h'.

HARD
JEE Main/Advance
IMPORTANT

A circle of constant radius 'r' passes through the origin O and cuts the axes of coordinates in points P and Q, then find the equation of the locus of the foot of the perpendicular from O to PQ.

HARD
JEE Main/Advance
IMPORTANT

The ends A, B of a fixed straight line of length 'a' and ends A' and B' of another fixed straight line of length 'b' slide upon the x-axis and y-axis (one end on axis of x and  the other on axis of y ). Find the locus of the centre of the circle passing through A, B, A' and B'