If x1, x2, x3 as well as y1, y2, y3 are in G P with same common ratio (not - Maths - Straight Lines

Question

If x1, x2, x3 as well as
y1, y2, y3 are in G P with same
common ratio (not equal to 1) then the points
(x1,y1) , (x2,y2), and
(x3,y3)
a lies on straight line
b lie on an ellipse
c lie on a circle
d are the vertices of a triangle
Please explain briefly

Gursheen kaur. · Accepted Answer

Let P (x1,y1) , Q (x2,y2), and R(x3,y3) Let a be first term and r be the common ratio of first G P then $x_{1} = a, x_{2} = a r & x_{3} = a r^{2}$ Let b be the first term and r be the common ratio of second G P then $y_{1} - b, y_{2} = b r & y_{3} = b r^{2} n o w, \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{b r - b}{a r - a} = \frac{b}{a} a l s o, \frac{y_{3} - y_{2}}{x_{3} - x_{2}} = \frac{b r^{2} - b r}{a r^{2} - a r} = \frac{b}{a} s l o p e o f P Q = s l o p e o f Q R h e n c e, t h e p t s P, Q, R l i e o n a s t r a i g h t l i n e$

If x1, x2, x3 as well as y1, y2, y3 are in G.P. with same common ratio (not equal to 1) then the points (x1,y1) , (x2,y2), and (x3,y3). a. lies on straight line b. lie on an ellipse c. lie on a circle d. are the vertices of a triangle Please explain briefly

If x₁, x₂, x₃ as well as y₁, y₂, y₃ are in G.P. with same common ratio (not equal to 1) then the points (x₁,y₁) , (x₂,y₂), and (x₃,y₃).

a. lies on straight line

b. lie on an ellipse

c. lie on a circle

d. are the vertices of a triangle

Please explain briefly