Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsCircle

If S: x^2+y^2+2 g x+2 f y+c=0 intersects both the lines x y-3 x=0 orthogonally and touches the circle x^2+y^2-6 x-12 y+36=0 externally, then:

Options

  1. AS neither intersects nor touches the x -axis
  2. Bradius of the circle S lies in (1,2)
  3. Cradius of the circle S lies in (2,3)
  4. Dequation of the transverse common tangent to both the circle is x+y-3 2 -9=0

Correct answer

B. radius of the circle S lies in (1,2)

Step-by-step solution

x(y-3)=0 (0,3) is the centre aligned & c₁ c₂=r₁+r₂ & 9+9 =r+3 & r=3( 2 -1) 1.2 aligned Transverse common tangent to both the circles x+y+k=0 gathered applying p=r k= 3 2 -9 x+y+3 2 -9=0 or x+y-3 2 -9=0 (rejected) gathered

Practice Circle on Quantrex Academy →

More from Circle

Match each entry in List-I to the correct entry in List-II and choose the correct option. List-I List-II (P) The circle with centre (1, 2) and touching the straight line 3x + 4y = 2026Consider the circle C: x^2+y^2-6x-8y-11=0 . Let a variable chord AB of the circle C subtend a right angle at the origin. If the locus of the foot of the perpendicular drawn from th 2026Let C be a circle having centre in the first quadrant and touching the x -axis at a distance of 3 units from the origin. If the circle C has an intercept of length 6 3 on y -axis, 2026Let the line x - y = 4 intersect the circle C: (x-4)^2 + (y+3)^2 = 9 at the points Q and R . If P( , ) is a point on C such that PQ = PR , then (6 + 8 )^2 is equal to __________. 2026Let the centre of the circle x^2 + y^2 + 2gx + 2fy + 25 = 0 be in the first quadrant and lie on the line 2x - y = 4 . Let the area of an equilateral triangle inscribed in the circl 2026Let P be a moving point on the circle x^2 + y^2 - 6x - 8y + 21 = 0 . Then, the maximum distance of P from the vertex of the parabola x^2 + 6x + y + 13 = 0 is equal to: 2026Suppose that two chords, drawn from the point (1, 2) on the circle x^2 + y^2 + x - 3y = 0 are bisected by the y -axis. If the other ends of these chords are R and S , and the mid p 2026Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x + (k-1)y + 3 = 0 and 2x + k^2 y - 4 = 0 . If the line x - y + 2026 Full Circle list All Most Important Selected Qs for JEE Advanced PYQs