Consider the family of circles `x^2+y^2-2x-2lambda-8=0` passing through two fixed points `Aa n dB` . Then the distance between the points `Aa n dB` is_____

Obtian the differential equation of the family of circles passing through the fixed points (a,0) and (-a,0), a ne 0

If 3a + 2b + 6c = 0 the family of straight lines ax+by = c = 0 passes through a fixed point . Find the coordinates of fixed point .

Find the equation of the chord of the circle x^2+y^2=a^2 passing through the point (2, 3) farthest from the center.

Consider a family of circles which are passing through the point (-1,1) and are tangent to the x-axis. If (h ,k) are the coordinates of the center of the circles, then the set of values of k is given by the interval. (a) kgeq1/2 (b) -1/2lt=klt=1/2 klt=1/2 (d) 0 < k < 1/2

Find the equation of line perpendicular to x - 2y +3=0 and passing through the point (3,-2) .

The two circles x^2+ y^2=r^2 and x^2+y^2-10x +16=0 intersect at two distinct points. Then

Prove that the family of lines represented by x(1+lambda)+y(2-lambda)+5=0,lambda being arbitrary, pass through a fixed point. Also find the fixed point.

Let a ,\ b ,\ c be parameters. Then the equation a x+b y+c=0 will represent a family of straight lines passing through a fixed point iff there exists a linear relation between a , b ,\ a n d\ c dot

Find the equation of the circle passing through the point (2,4) and has its centre at the intersection of x-y =4. and 2x +3y=-7.

Find the equation of a curve passing through the point (–2, 3), given that the slope of the tangent to the curve at any point (x, y) is 2x/y^2