#Showthat x²+y²-14x+6y+33=0, x²+y²+30x-2y+1=0 have 4 common tangents. Find point of intersection

#AIMSDARETOSUCCESS #AIMSDTSSHORTS #Showthat x^2+y^2-14x+6y+33=0, x^2+y^2+30x-2y+1=0 have exactly 4 common tangents. Find the intersection of those tangents If the circle x^2 + y^2 + 6x - 8y + c = 0 has radius 6 then find the value of “c”    • 1#CIRCLES #If the circle x² + y² + 6x - 8y...   Find “a” if 2x^2 + ay^2 – 3x + 2y – 1 = 0 represents a circle. Find its radius.    • 2#CIRCLES #Find “a” if 2x² + ay² – 3x + 2y...   If x^2 + y^2 + 2gx + 2fy = 0 represents a circle with centre (–4,–3) then find g, f, radius    • 3#If x² + y² + 2gx + 2fy = 0 represents a ...   Find the equation of the circle passing through (2, – 1) and having the centre at (2, 3)    • 4#CIRCLES #Find the equation of the circle...   Find the equation of circle which is concentric with x^2+y^2–6x–4y–12=0, passing through (–2,14)    • 5#Find the equation of circle which is con...   Find the other end of the diameter of the circle x^2 + y^2–8x–8y+27=0 if one end of it is (2,3)    • 6#Find the other end of the diameter of th...   Obtain the parametric equation of the circle x^2 + y^2 = 4    • 7#CIRCLES #Obtain the parametric equation ...   Obtain the parametric equation of the circle x^2 + y^2 – 6x + 4y – 12 = 0    • 8#CIRCLES #Obtain the parametric equation ...   Find the equation of the circle whose extremities ends of the diameter are (1, 2), (4, 6)    • 9#CIRCLES #Find the equation of the circle...   Locate the position of the point (1, 2) with respect to the circle x^2 + y^2 + 6x + 8y - 96 = 0    • 10#Locate the position of the point (1, 2)...   Locate the position of the point (1, 5) with respect to the circle x^2 + y^2 - 2x - 4y + 3 = 0    • 11#Locate the position of the point (1, 5)...   Find the power of the point P (2, 3) with respect to the circle x^2 + y^2 – 2x + 8y – 23 = 0    • 12#Find the power of the point P (–1,1) wi...   If the length of the tangent from (2, 5) to the circle x^2 + y^2 – 5x + 4y + k = 0 is √37 then find k    • 13#If the length of tangent from (2, 5) to...   Find the equation of the normal at P (1, 1) of the circle 2x^2 + 2y^2 – 2x – 5y + 3 = 0    • 14#CIRCLES #Find the equation of the norma...   Find the equation of chord of contact of the point P (1, 1) with respect to the circle x^2 + y^2 – 9 = 0    • 15#Find the equation of chord of contact o...   Find the equation of the polar of the point (2, 3) with respect to the circle x^2 + y^2 + 6x + 8y - 96 = 0    • 16#Find the equation of the polar of the p...   Find the equation of the tangent to the circle x^2 + y^2 + 4x + 6y – 39 = 0 at the point (–6, –9)    • 17#Find the equation of the tangent to the...   Showthat x^2+y^2-8x-6y+21=0, x^2+y^2-2y-15=0 have exactly 2 common tangents. Find the intersection of those tangents    • #Showthat x²+y²-8x-6y+21=0, x²+y²-2y-15=0 ...   Showthat x^2+y^2-14x+6y+33=0, x^2+y^2+30x-2y+1=0 have exactly 4 common tangents. Find the intersection of those tangents    • #Showthat x²+y²-14x+6y+33=0, x²+y²+30x-2y+...   The equation of the circumcircle whose sides are 2x + y = 4, x + y = 6, x + 2y = 5    • #Find The the circumcircle whose sides are...   Find the equation of the circle passing through origin and making intercepts 4 units on X axis, making intercepts 3 units on Y axis    • #The eqn of circle passing through origin,...   Find the equation of the circle passing through origin and making intercepts 6 units on X axis, making intercepts 4 units on Y axis    • #The eqn of circle passing through origin,...   If (2, 0), (0, 1), (4, 5), (0, c) are concyclic then find c    • #If (2, 0), (0, 1), (4, 5), (0, c) are con...   Find the equation of the circle which passing through two points (4, 1), (6, 5) and having Centre on the line 4x + 3y - 24 = 0    • #Find the equation of #Circle passing thro...   Find the equation of the circle passing through three points (1, 1), (2, – 1), (3, 2)    • #Find the equation of the #Circle passing ...   Showthat x^2+y^2-4x-6y-12=0, 5x^2+5y^2-8x-14y-32=0 touch each other. Find their point of contact    • #Showthat x²+y²-4x-6y-12=0, 5x²+5y²-8x-14y...   Show that the pair of circles x^2+y^2-4x-6y-12=0, x^2+y^2+6x+18y+26=0 touch each other. Find the point of contact and the equation of common tangent    • #Showthat x²+y²-4x-6y-12=0, x²+y²+6x+18y+2...   Show that x^2+y^2-6x-2y+1=0, x^2+y^2+2x-8y+13=0 touch each other. Find the point of Contact and the equation of common tangent at their point of contact    • #Showthat x²+y²-6x-2y+1=0, x²+y²+2x-8y+13=...   Show that the pair of circles x^2+y^2-6x-9y+13=0, x^2+y^2-2x-16y=0 touch each other. Find the point of Contact and the equation of the common tangent at this point of contact    • #Showthat x²+y²-6x-9y+13=0, x²+y²-2x-16y=0...   Find the Direct Common Tangent of the Pair of Circles x^2+y^2+22x-4y-100=0, x^2+y^2-22x+4y+100=0    • 13#Find the Direct Common Tangent of the P...   Find the equation of Pair of Transverse Common Tangents to the Pair of Circles x^2+y^2-4x-10y+28=0, x^2+y^2+4x-6y+4=0    • 14#Find eq of Pair of Transverse Common Ta...