ಪ್ರಮೇಯ: P(x_1,y_1) ಮತ್ತು Q(x_2,y_2) ಎರಡು ಬಿಂದುಗಳ ನಡುವಿನ ಅಂತರವನ್ನು sqrt((x_2-x_1)^2+...

Theorem: The distance between two points P(x_(1);y_(1)) and Q(x_(2);y_(2)) is given by sqrt(x_(-)2-x_(-)1)^(^^)2+(y_(-)2-y_(-)1)^(^^)2)

The ratio in which the line segment joining P(x_1, y_1) and Q(x_2, y_2) is divided by x-axis is y_1: y_2 (b) y_1: y_2 (c) x_1: x_2 (d) x_1: x_2

If theta\ is the angle which the straight line joining the points (x_1, y_1)a n d\ (x_2, y_2) subtends at the origin, prove that tantheta=(x_2y_1-x_1y_2)/(x_1x_2+y_1y_2)\ a n dcostheta=(x_1x_2+y_1y_2)/(sqrt(x1 2+y1 2x2 2+y2 2))

y=sqrt((x^(2)+x+1)/(x^(2)-x+1))

Prove that the line passing through the points (x_(1),y_(1)) and (x_(2),y_(2)) is at a distance of |(x_(1)y_(2)-x_(2)y_(1))/(sqrt((x_(2)-x_(1))^(2)+(y_(2)-y_(1))^(2)))| from origin.

If the circle x^2 + y^2 = a^2 intersects the hyperbola xy=c^2 in four points P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3), S(x_4, y_4) , then : (A) x_1 + x_2 + x_3 + x_4 = 0 (B) y_1 + y_2 + y_3 + y_4 = 0 (C) x_1 x_2 x_3 x_4= c^4 (D) y_1 y_2 y_3 y_4 = c^4

If the points (x_1, y_1), (x_2, y_2) and (x_3, y_3) be collinear, show that: (y_2 - y_3)/(x_2 x_3) + (y_3 - y_1)/(x_3 x_2) + (y_1 - y_2)/(x_1 x_2) = 0

The equation to the chord joining two points (x_1,y_1) and (x_2,y_2) on the rectangular hyperbola xy=c^2 is: (A) x/(x_1+x_2)+y/(y_1+y_2)=1 (B) x/(x_1-x_2)+y/(y_1-y_2)=1 (C) x/(y_1+y_2)+y/(x_1+x_2)=1 (D) x/(y_1-y_2)+y/(x_1-x_2)=1

Find the distance between points P(x_1, y_1) and Q(x_2, y_2) : PQ is parallel to x-axis