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

Let the circle S: x^2+y^2-a x-b y+c=0 intersects the pair of straight lines x y-4 x-3 y+12=0 orthogonally and the circle lies in the first quadrant. If S touches the circle S₁:(x-3)^2+y^2=r^2, r N , then find the sum of all possible values of r .

Correct answer

28

Step-by-step solution

aligned & x y-3 x-4 y+12=0 & (x-3)(y-4)=0 x=3 and y=4 & S: x^2+y^2-6 x-8 y+c=0 aligned For R=3, r=1 and 7 For R=2, r=2 and 6 For R=1, r=3 and 5 For R=0, r=4 Sum of all possible values of r=1+2+3+4+5+6+7=28

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