The equation of the chord joining two po...

The equation of the chord joining two points `(x_(1),y_(1)) and (x_(2),y_(2))` on the rectangular hyperbola `xy=c^(2)` is

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The equation to the chord joining two points (x_1,y_1)a n d(x_2,y_2) on the rectangular hyperbola x y=c^2 is:

Show that the equation of the straight line joining the points (x_(1),y_(1))and(x_(2),y_(2)) can be expressed in the form (x-x_(2))(y-y_(1))=(x-x_(1))(y-y_(2)) .

Prove that the square of the distance between the two points (x_(1), y_(1)) and (x_(2), y_(2)) of the circle x^(2) + y^(2) = a^(2) is 2(a^(2) - x_(1)x_(2) - y_(1)y_(2)) .

Show that the equation of the chord of the parabola x^(2) = 4ay joining the points (x_(1),y_(1)) ann (x_(2),y_(2)) on it is (x-x_(1))(x-x_(2))=x^(2)-4ay .

Show that the equation of the chord of the parabola y^(2) = 4ax through the points (x_(1),y_(1)) and (x_(2),y_(2)) on it is (y-y_(1))(y-y_(2)) = y^(2) - 4ax

The points P divides the line - segment joining the points A(x_(1),y_(1))andB(x_(2),y_(2)) in the ratio m : n . If P lies on the line ax+by +c=0 , prove that, (m)/(n)=-(ax_(1)+by_(1)+c)/(ax_(2)+by_(2)+c) .

The line y=mx+1 touches the curves y=-x^(4)+2x^(2)+x at two points P(x_(1),y_(1)) and Q(x_(2),y_(2)) . The value of x_(1)^(2)+x_(2)^(2)+y_(1)^(2)+y_(2)^(2) is

The straight line joining the points p(x_(1),y_(1))andQ(x_(2),y_(2)) makes an angle theta with the positiv direcction of the x-axis prove that , x_(2)=x_(1)+rcostheta and y_(2)=y_(1)+rsintheta where r=overline(PQ) .

Show that the equation of the chord of the parabola y^2=4ax through the points (x_1,y_1) and (x_2,y_2) on its (y-y_1)(y-y_2)=y^2-4ax.

If the tangent at point P(h, k) on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 cuts the circle x^(2)+y^(2)=a^(2) at points Q(x_(1),y_(1)) and R(x_(2),y_(2)) , then the vlaue of (1)/(y_(1))+(1)/(y_(2)) is

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