A line is drawn through a fixed point P(...

A line is drawn through a fixed point` P(alpha,beta)`to cut the circle `x^2+y^2=r^2` at A and B. Then PA.PB i equal to

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Tangents PQ and PR are drawn from the point (alpha, beta) to the circle x^(2)+y^(2)=a^(2) . Show that the area of Delta PQR is (a(alpha^(2)+ beta^(2)-a^(2))^(3//2))/(alpha^(2)+ beta^(2)) .

A moving straight line always passes through a fixed point (alpha,beta) .Prove that the locus of the middile point of the portion of the line intercepted between the axes is alpha/x+beta/y=2

If a circle passes through the point (a,b) and cuts the circle x ^(2) +y^(2) =p^(2) orthogonally, then the equation of the locus of its centre is-

If a circle passes through the point (a, b) and cuts the circle x^2+y^2=K^2 orthogonally then the equation of the locus of its centre is

A moving straight line always passes through a fixed point (alpha , beta) . Prove that the locus of the middle point of the portion of the line intercepted between the axes is (alpha)/(x)+(beta)/(y) = 2 .

Through a fixed point (h, k) secants are drawn to the circle x^2 +y^2 = r^2 . Then the locus of the mid-points of the secants by the circle is

A variable straight line AB intersecting the x and y-axies at A and B always passes through a fixed point (alpha,beta) . Find the locus of the point dividing AB in the ratio 2:1 .

The straight line y=mx+c cuts the circle x^2+y^2=a^2 at real points if

If the axis are transferred to parallel axis throught the point (alpha,beta) , then equation of the circle (x-alpha)^(2)+(y-beta)^(2)=a^(2) reduces to the form-

A moving st.line always passes through a fixed pt. (alpha,beta) .Prove that the locus of the middle point of the portion of the line intercepted between the axes is alpha/x+beta/y=2

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