Analytic Geometry Answers

a) Give parametric equation (point-direction form) of the line which lies on both of the planes:

x + y + z = 1 and −x + 2y + 10z = 2. What is the direction d of this line?

b) Let n1 and n2 be the normal vectors to the two given planes. Without actual computation,

describe the relationship between d and n1 × n2.

In the coordinate plane the point X(4,1)is translated to the point X(5,-1) under the same translation the points Y(2,5)and Z(0,3) are translated to Y and Z. What are the coordinates of Y and Z

Find the equation of the hyperbola with foci at (1,2) (1,6) and vertices at (1,3) (1,5)

P is a point on the parabola whose ordinate

equals its abscissa. A normal is drawn to the parabola at

P to meet it again at Q. If S is the focus of the parabola

then the product of the slopes of SP and SQ is-

One side of a square lies along the straight line4𝑥 + 3𝑦 = 26. The diagonals 

of the square intersect at the point (−2,3).

Find;

(a) The coordinates of the vertices of the square.

(b)The equation of the sides of the square which are perpendicular to the given 

line.

Given point A (2 , -3) in a plane; find the coordinates of its image:

a) Under enlargement about ( -3 , 1 )with scale factor 2; (3marks)

b) Under rotation of center ( -2 , 1 ) and angle θ=π/6

Find the angle between the vectors a and b given that

a = 3i + 4j and b = 5i – 12j (correct to 1d.p)

Given the parabola (y-1)² = 1/2(x-3),

find;

i. The coordinates of the vertex

ii. The coordinates of the focus

iii. The equation of the directrix

iv. The equation of the axis of symmetry

v. The ends of the latus rectum

vi. The parametric equations of the parabola

vii. Sketch the parabola, clearly showing the focus, vertex, directrix, axis of symmetry, and the x-intercept.

Given the equation of a circle as X^2+Y^2+4x-6y=-