Find the two points of intersection of the circles, see handout #4 signment 11Due date : Friday, December 11Section 22.4, Page 707#1, 2, 6*, 7*, 14, 15, 17.*Note: The vertex is at the origin in these problems.Required Additional ExercisesExercises #1 – 5 (below).1. Find the distance from the point to the given line by using the distance theoremhttp://mypages.iit.edu/~maslanka/PointtoLine.pdf(a) 2 x – 4 y + 2 = 0 ; (1,3)(b) 4х+5у-3-0; (-2,4)2. Find the distance between the parallel lines:L: 2 x- 5 y +3 = 0; L2: 2 x – 5 y + 7 = 0.(Hint: It suffices to compute the distance from any particular point P, on L to the line La.)3. Find the equation of the line L bisecting the angle from Li to La givenLi: 3 x – 4 y – 2 = 0 ;Hint: Note that if P = ( x , y) is any point on the bisector L then its coordinates satisfyL2: 4 x – 3 y + 4 = 0.the condition:|A,x + B1y+ C¡| _ |A,x + B,y+ C¿|VA,? + B,2VA,² + B,²|A,² + B,² · ( Aµx + B¡y+ C;) = ± VA,² + B,² · (A,x + B2y+ C,) (*)where L: A,x+B,y +C, =o and L2: A,x + B,y + C, = 0 .The solutions to (*) yield the equations of both lines bisecting the angles between L, and L2.4. Find the two points of intersection of the circles:x² + y 2 + 5 x + y – 26 = 0 ; x² + y² + 2 x – y – 15 = 0.5. Find the equation of the parabola P with focus F = (1,1) and the directrixD: x + y = 0 in two ways:(a) By using the fact that : Q = ( x , y ) on P → d(Q,F ) = d ( Q , D ).Hint: Square both sides of your equation for the parabola in order to eliminate thesquare roots and absolute values and then simplify it.(b) By rotating the parabola y² =2 z x by 45° about its axis and translating1its graph + units horizontally and +; units vertically.Hint: Transform the equation of the parabola to polar coordinates before rotatingthis curve. Then transfer back to xy-coordinates in order to translate theequation of the rotated parabola. Refer to the handout:http://mypages.iit.edu/~maslanka/R&T_Thrms.pdf for details on rotationand translations theorems.

Given, The equations of the circles are, x2+y2+5x+y-26=0 ....... (1) and x2+y2+2x-y-15=0…

Answered: 4. Find the two points of intersection…

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4. Find the two points of intersection of the circles: x² + y 2 + 5x + y – 26 = 0 ; x² + y ² + 2 x – y – 15 = 0.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter4: Quadrilaterals

Section4.4: The Trapezoid

Problem 24E: The state of Nevada approximates the shape of a trapezoid with these dimensions for boundaries: 340...

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Question

Find the two points of intersection of the circles, see handout #4

signment 11
Due date : Friday, December 11
Section 22.4, Page 707
#1, 2, 6*, 7*, 14, 15, 17.
*Note: The vertex is at the origin in these problems.
Required Additional Exercises
Exercises #1 – 5 (below).
1. Find the distance from the point to the given line by using the distance theorem
http://mypages.iit.edu/~maslanka/PointtoLine.pdf
(a) 2 x – 4 y + 2 = 0 ; (1,3)
(b) 4х+5у-3-0; (-2,4)
2. Find the distance between the parallel lines:
L: 2 x- 5 y +3 = 0; L2: 2 x – 5 y + 7 = 0.
(Hint: It suffices to compute the distance from any particular point P, on L to the line La.)
3. Find the equation of the line L bisecting the angle from Li to La given
Li: 3 x – 4 y – 2 = 0 ;
Hint: Note that if P = ( x , y) is any point on the bisector L then its coordinates satisfy
L2: 4 x – 3 y + 4 = 0.
the condition:
|A,x + B1y+ C¡| _ |A,x + B,y+ C¿|
VA,? + B,2
VA,² + B,²
|A,² + B,² · ( Aµx + B¡y+ C;) = ± VA,² + B,² · (A,x + B2y+ C,) (*)
where L: A,x+B,y +C, =o and L2: A,x + B,y + C, = 0 .
The solutions to (*) yield the equations of both lines bisecting the angles between L, and L2.
4. Find the two points of intersection of the circles:
x² + y 2 + 5 x + y – 26 = 0 ; x² + y² + 2 x – y – 15 = 0.
5. Find the equation of the parabola P with focus F = (1,1) and the directrix
D: x + y = 0 in two ways:
(a) By using the fact that : Q = ( x , y ) on P → d(Q,F ) = d ( Q , D ).
Hint: Square both sides of your equation for the parabola in order to eliminate the
square roots and absolute values and then simplify it.
(b) By rotating the parabola y² =2 z x by 45° about its axis and translating
1
its graph + units horizontally and +; units vertically.
Hint: Transform the equation of the parabola to polar coordinates before rotating
this curve. Then transfer back to xy-coordinates in order to translate the
equation of the rotated parabola. Refer to the handout:
http://mypages.iit.edu/~maslanka/R&T_Thrms.pdf for details on rotation
and translations theorems.

Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.

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