Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2020MathematicsCircleActual

In the given figure, the equation of the larger circle is x²+y²+4 y-5=0 and the distance between centres is 4 . Then the equation of smaller circle is

Options

  1. A(x- 7 )²+(y-1)²=1
  2. B(x+ 7 )²+(y-1)²=1
  3. Cx²+y²=2 7 x+2 y
  4. DNone of these

Correct answer

A. (x- 7 )²+(y-1)²=1

Step-by-step solution

We have x²+y²+4 y-5=0 . Its centre is C ₁(0,-2) r ₁= 4+5 =3 . Let C ₂( ~h , k ) be the centre of the smaller circle and its radius r ₂ . Then C ₁ C ₂=4 h ²+( k +2)² =3+ r ₂=4 r ₂=1 But k = r ₂=1 [it touches x -axis From eq (1), 4= h ²+(1+2)² 16= h ²+9 h ²=7 h = 7 Since h >0 h = 7 Hence, required circle is (x- 7 )²+(y-1)²=1

Practice Circle on Quantrex Academy →

More from Circle

The locus of the mid-point of a chord of the circle x^2+y^2=4 , which subtends a right angle at the origin is 2024If p and q be the longest and the shortest distance respectively of the point (-7,2) from any point ( , ) on the curve whose equation is x^2+y^2-10 x-14 y-51=0 , then G.M. of p 2024From a point A (0,3) on the circle (x+2)^2+(y-3)^2=4 , a chord A B is drawn and it is extended to a point Q such that A Q=2 A B . Then the locus of Q is 2024The equation of the circle with centre (0,2) and radius 2 is x^2+y^2-m y=0 . The value of m is 2023A circle touches both the y -axis and the line x+y=0 . Then the locus of its center is 2023For each parabola y=x^2+p x+q , meeting coordinate axes at 3-distinct points, if circles are drawn through these points, then the family of circles must pass through 2022The locus of the mid-point of the chord if contact of tangents drawn from points lying on the straight line 4 x-5 y=20 to the circle x^2+y^2=9 is 2022The equation of the circle, which touches the line y=5 and passes through (-1,2) and (1,2) is 2021 Full Circle list All BITSAT PYQs