help@askiitians.com

1800-150-456-789

Analytical Geometry> Find the equations of the circles whose c...

question mark

Find the equations of the circles whose centers lie on the line 4x + 3y = 2 and which touch the lines x + y + 4 = 0 and 7x - y + 4 = 0

There are 2 solutions to this question...

Utkarsh , 10 Years ago

Grade

3 Answers

Ravi

Last Activity: 10 Years ago

This will give 2 values of theta. Hence, 2 values of coordinates of the centre. Use the length of prependicular to find the 2 corresponding radii. This should give the 2 eqns of circles satisfying the conditions mentioned.

Utkarsh

Last Activity: 10 Years ago

Thank you so much Sir!!!

Shrutik

Last Activity: 7 Years ago

Let the centre of the circle be C (h,k).

Since the Centre lies on the line 4x+3y=2, we get 4h+3k=2

h = ( 2 – 3k ) / 4 …... Eqn (1)

Since the lines 7x-y+4=0 and x+y+4 are touching the circles ( ie they are tangents ), let’s use the formula : Distance of point C(h,k) from these lines to get the radius as :

$\displaystyle \left | 7h-k+4 \right | / \sqrt{7*7+1*1}= \left | h+k+4 \right|/\sqrt{1*1+1*1}$ …...Eqn (2)

Substitute Eqn 1 in Eqn 2 to solve for k, giving k = -2 … thus h = 2 for +ve sign of Modulus and k = 6 and h = -4 for -ve sign of modulus.

Thus, the 2 centres are C₁(2,-2) and C₂(-4,6). Radii of these 2 circles are 4/sqrt(2) and 6/sqrt(2) respectively.

Finally, using Centre -radius form, we get the 2 equations as

x² + y² -4x+4y = 0 and x²+y²+8x-12y+34=0

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

The locus of the point represented by x= t^2 +t+1 and y=t^-t+1 is

analytical geometry

0 Answer Available

Last Activity: 2 Years ago

show that the centroids of the triangles of which three perpendiculars lie along the lines y=m1x,y=m2x,y=m3x lie on y(3+m2m3+m3m2+m1m2)=x(m1+m2+m3+3m1m2m3)

analytical geometry

0 Answer Available

Last Activity: 3 Years ago

show that the equation (ab-h²)(ax²+2hxy+by²+2gx+2fy)+af²+bg²-2fgh=0 represent a pair of straight lines and that these straight lines form a rhombus with the lines ax²+2hxy+by²=0

analytical geometry

0 Answer Available

Last Activity: 3 Years ago

A circle has its center on straight line 5x-2y+1=0 and cuts the x axis at two points whose absciasse are -5,3 find equation of the circle and it's radius.

analytical geometry

0 Answer Available

Last Activity: 3 Years ago

Prove that ax^2+by^2+cz^2 +2ux+2vy+2wz+d=0 represent a cone if u^2/a+v^/b+w^2/c=d

analytical geometry

0 Answer Available

Last Activity: 3 Years ago

View all Questions