the eccentricity of the locus of the locus of point (3h+2,k), where (h,k) lies on the ellipse x2+y2=1, is
Find the equation of the small circle that touches the circle x2+y2=1 and passes through the point (4,3)˙
The circle x2+y2−4x−4y+4=0 is inscribed in a variable triangle OAB˙ Sides OA and OB lie along the x- and y-axis, respectively, where O is the origin. Find the locus of the midpoint of side AB˙
Two fixed circles with radii r1andr2,(r1>r2) , respectively, touch each other externally. Then identify the locus of the point of intersection of their direction common tangents.
Let A (-2,2)and B (2,-2) be two points AB subtends an angle of 45∘ at any points P in the plane in such a way that area of ΔPAB is 8 square unit, then number of possibe position(s) of P is
If the two circles 2x2+2y2−3x+6y+k=0 and x2+y2−4x+10y+16=0 cut orthogonally, then find the value of k .
The tangent to the circle x2+y2=5 at (1,−2) also touches the circle x2+y2−8x+6y+20=0 . Find the coordinats of the corresponding point of contact.
The lengths of the tangents from P(1,−1) and Q(3,3) to a circle are 2 and 6 , respectively. Then, find the length of the tangent from R(−1,−5) to the same circle.