The intersection of the plane (Orange color) with double cone has been shown in the following figures. You are required to just right the name of the intersection curve (Blue curves).

Q: Find the intersection point and draw the curve

A: The given curves are y1=39-3x2 and y2=x+22.

Q: nd the condit. on if the circle whose equation a x² + y² + c² = 2ax = 0 and x² + y² + c² = 2b y = 0…

A: The two circles are x2+y2+c2=2ax=0 and x2+y2+c2=2by=0.centers:C1(a,0),C2(0,b)radii:r1=a2=c2,r2=b2-c2

Q: Identify the vertex, focus, directerix and length of the latus rectum. y= 1/14x2

A:

Q: (a+2) + (y-1)² = 4 Hint: Find the center and radius of your circle first. Then choose

A:

Q: Find the center and radius of the circle x2 + y2 = 6y + 16.

A:

Q: X is the center of one circle, Y is the center of the other. How do you know that triangle XYZ is…

A: We will show how the triangle XYZ is an equilateral triangle as following

Q: Which of the following points lies on the circle (x-2)2 + (y-3)2 5? Select one: a. (3,5) b. (5, 3)…

A:

Q: What is the equation of a circle with its center at (0,–2) and passing through the point (3, –5)?

A: Given,          The equation of a circle with its center at 0,-2 and passing through the…

Q: Is the point (-15, 15) on the circle defined by (x+15)+(y-15) = 100? Yes No X Ś

A: To determine whether the given point lies on the circle or not.

Q: Write the standard equation for the circle whose center is at (1,1) and whose radius is 5.

A: With center (h,k) and radius=r (x-h)2+(y-k)2=r2

Q: Which of the following points is on the circle below O (10, 6) O (8 , 121) O (5, 5) O (54, JA6)

A: Given query is to find the point on the circle.

Q: Use a rectangular coordinate system to graph the circle with center (1, -1) and radius 1.

A:

Q: Find the distance from (-5, 9, -12) to each of the following: 1. The xy-plane. Answer: 2. The…

A:

Q: Which are the center and radius of the circle with equation (x + 5)- + (y – 4)² = 9? O A. (-5, -4);…

A: Option C is correct. Please see below for solution

Q: Which is an equation for the circle with a center at (-2,3) and a radius of 3?

A: Equation of circle is given by: where (h,k) is center and r is radius.

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.