Analytic Geometry Answers

Find the equations of the line through (1,3, 4 ) and parallel to the line joining the points (−4, 5, 3) and (8, 9, 7)

Prove that the length of the chord of a parabola which passes through the focus and which is inclined at 30° to the axis of the parabola is four times the length of the latus rectum.

Prove that the equation of a line through (𝑥₁ , 𝑦₁) and (𝑥₂ , 𝑦₂) can be expressed in the form determinant

x y 1

x₁ y₁ 1

x₂ y₂ 1

= 0

Let 𝑃 be the midpoint of the line segment joining the points 𝐴(𝑎 + 𝑏, 𝑏) and 𝐵(𝑎 − 𝑏, 𝑎 + 𝑏). Find the slope of the line passing through 𝑃 and 𝑄 (𝑏, −𝑎/2) .

Prove that the conic passing through the points of intersection of two rectangular hyperbolas is also a rectangular hyperbola.

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

A truck hauling a cylindrical steel ta

nk has to pass under an overhead parabolic arch bridge

which has span of 7.32m and 6.10m high. If the tank is 1.83m in

diameteris placed in the truck with sides vertical, and the top of the tank is 3.05m above the street level, can the truck pass the bridge? If so,what is the smallest clearance from the top of the tank

Circles has radius 5 and tangent to the line 3x+4y=24 at the point (2, 412⁄). Illustrate thenfindthe equations of thecircles