If {x_1}, {x_2}, {x_3} and {y_1}, {y_2}, {y_3 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the common ratio be $r$. Since ${x_1}, {x_2}, {x_3}$ are in $G$.$P$.,we have ${x_2} = {x_1}r$ and ${x_3} = {x_1}r^2$.Similarly,since ${y_1}, {

Vedclass · Accepted Answer

Lie on a straight line

Vedclass · Answer

(A) Let the common ratio be $r$. Since ${x_1}, {x_2}, {x_3}$ are in $G$.$P$.,we have ${x_2} = {x_1}r$ and ${x_3} = {x_1}r^2$.Similarly,since ${y_1}, {y_2}, {y_3}$ are in $G$.$P$. with the same common ratio $r$,we have ${y_2} = {y_1}r$ and ${y_3} = {y_1}r^2$.The points are $P_1 = ({x_1}, {y_1})$,$P_2 = ({x_1}r, {y_1}r)$,and $P_3 = ({x_1}r^2, {y_1}r^2)$.Notice that for all points,the ratio of the $y$-coordinate to the $x$-coordinate is constant: $\frac{{y_1}}{{x_1}} = \frac{{y_1}r}{{x_1}r} = \frac{{y_1}r^2}{{x_1}r^2} = m$ (where $m = \frac{{y_1}}{{x_1}}$).This implies that all three points satisfy the linear equation $y = mx$,which represents a straight line passing through the origin.

If ${x_1}, {x_2}, {x_3}$ and ${y_1}, {y_2}, {y_3}$ are both in $G$.$P$. with the same common ratio,then the points $({x_1}, {y_1}), ({x_2}, {y_2})$ and $({x_3}, {y_3})$:

Similar Questions

Consider the fourteen lines in the plane given by $y=x+r$ and $y=-x+r$,where $r \in \{0, 1, 2, 3, 4, 5, 6\}$. The number of squares formed by these lines,whose sides are of length $\sqrt{2}$,is:

If the straight line $L \equiv 3x+4y-k=0$ cuts the line segment joining the points $P(2,-1)$ and $Q(1,1)$ in the ratio $4:1$,then the equation of the line parallel to the line $y=x$ and concurrent with the lines $PQ$ and $L=0$ is

Let the line $2x + 3y = 18$ intersect the $Y$-axis at $B$. Suppose $C(\neq B)$,with coordinates $(a, b)$,is a point on the line such that $PB = PC$,where $P = (10, 10)$. Then,$8a + 2b$ equals

$A$ straight line $x/a - y/b = 1$ passes through the point $(8, 6)$ and cuts a triangle of area $12 \text{ sq units}$ from the axes of coordinates. The equations of the straight lines are

Find the equation of the line passing through the intersection of the lines $x - 3y + 1 = 0$ and $2x + 5y - 9 = 0$ and whose distance from the origin is $\sqrt{5}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module