Analytic Geometry Answers

In the Cartesian plane, two vertices of a square have coordinates (3 ; 4) and ( -2 ; - 1). One of the other two vertices, has coordibates

If the position vector of A and B are 3 −→a − 7 −→b − 7 −→c and 5 −→a + 4 −→b + 3−→c , nd −→AB and determine its magnitude and direction cosines.

The coordinates of the image of 𝑃(𝑥, 𝑦) when 𝑦 = 𝑓(𝑥) is transformed to

𝑦 = 2 𝑓(𝑥 − 3) − 1 are 𝑃′

(2, 3). Find the original point (𝑥, 𝑦).

<e> Find the equation of the sphere touching the plane 8𝑥 + 5𝑦 + 3𝑧 + 1 = 0 at (3, −1, −1) and cutting the sphere 𝑥² + 𝑦² + 𝑧² − 2𝑥 + 𝑦 − 𝑧 − 6 = 0 orthogonally.

How to find the coordinate of p and q if the circle cuts the x-axis at the points p and q in 2x^2 +2y^2 -8x +5y -10=0

Find the equation of the line which is perpendicular to 4𝑦=5𝑥−8 and passing through (2,3).

𝐴(1,−2) is a point on the circle (𝑥−3)2+ (𝑦+1)2= 5

a. State the coordinates of the centre of the circle and hence find the coordinates of the point 𝐵 where 𝐴𝐵 is the diameter of the circle.

b. 𝐶(2,1) also lies on the circle. Use coordinate geometry to verify that angle 𝐴𝐶𝐵 = 900

in the triangle ABC having vertices at A(-2,5), B(6,1) and C(-2,-3), find the length of the median from vertex B to side AC.

x=5^1/4 5^-1/4 y=5^1/4 - 5^-1/4 prove that 5(x² y²)²=144?

a. The points 𝐴,𝐵 and 𝐶 have co-ordinates (−1,2),(1,1) and (2,3) respectively. Sketch the triangle 𝐴𝐵𝐶 .By calculating the lengths of the sides of this triangle, determine if it is scalene, isosceles, or equilateral.

b. Find the distance 𝑀𝐵, where 𝑀 is the midpoint of 𝐴𝐶, and hence find the area of the triangle 𝐴𝐵𝐶.