IV. Plot the vertex and the endpoints of the latus rectum and sketch the graph of the following equations. 26. (y – 7)2 = x + 3 27. x = -(y – 1)² + 12

Q: 14. Which equation represents the given parabola? O y = -4(x – 4)² + 5 O y = }(x – 4)² + 5 O y =…

A: First option is correct.

Q: 8. Find the equation of the circle which is tangent to the y- axis, which passes through the point…

A: To find equation of Circle which is tangent to y axis, passes through point (-1,-1) and it's centre…

Q: 2a? + 2y? + 8x + 4y + 8 = 0 is the equation of a circle with center (h, k) and radius r for: h and k…

A: The equation of the circle 2x2+2y2+8x+4y+8=0, we have to find the center and radius of this equation…

Q: What is the equation of the graph? A. y = 4cos (3x) В. у %3D 4sin (3х) С. у %3D Зсos (4x) D. y =…

A:

Q: Determine the graph of the equation a² + y² + 2² - 6x + 2y - 4z + 19 = 0. O Sphere O Point O Empty…

A: Given :x2+y2+z2-6x+2y-4z+19=0

Q: Which of the following is the shortest distance from the point (5, 0) to the curve y = /2x 5 a) 2 b)…

A:

Q: I. Sketch and identify the graph of the following equations in R³ : 1. 9a2 + 4y2 = 36 %3D

A: The standard form of the ellipse is x2a2+y2b2=1. The given equation is 9x2+4y2=36.

Q: 7. The radius of the circle whose equation x + 6x + y – 6y – 7 = 0 is

A: Your answer Radius =5

Q: Where does the line x = 1 + 3t, y = 2−t intersect (a) the x-axis (b) the y-axis (c) the parabola y =…

A: Parametric equations are a set of equations where 2 or more variables are dependent on one single…

Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-…

A: Solving two equations

Q: The r coordinate of the point of intersection between the two curves y = e2Az and y = 1 is (Write…

A:

Q: 3. the lines r = y² – 2 and r = y and whose lies between z = x + 2 and %3D =y-2 whith the graph

A: Given equations are: x=y2-2 and x=y lying between z=x+2 and z=y-2. Since the given equations are in…

Q: Q3) For what values of n the line y = -x + n intersects the ellipse +=1 at two poin 20

A:

Q: Suppose (P, Q) is the point on the graph of y = Vx closest to (1, 0). What is the value of P+ Q?…

A: In this we have to find the closest distance and then sum up. So I'm providing hand written solution…

Q: 5 which of the followinginan equation of the tengentto the graphefy=x at y=3? x2 A) ye 33X-63 6)yこ…

A:

Q: 12. A circle in the xy-plane has equation (x + 3)² + (y - 1) = 25. Which of the following points…

A: According to the problem, we have

Q: 13. Find the equation of the circle. X(G-1)?+ (y+5)* - 16 C. (x+ 1)* + (v-5)* - 16 С. B. (x+1)°+ (y-…

A: Let's find.

Q: (a) y" + 7y + 12y = 0, y(0) = -1, y(0) = 0 %3D %3D

A: We have to find general solution and it's sketch.

Q: photo attached

A: From the given statement,

Q: 9) Find the point on the parabola y = 10-x² closest to the point (0, 5.5).

A: Given question:- Find the point on parabola y= 10-x2 closest to point (0,5.5)

Q: 2 TL (21) 3.The vertex is at (4,-4) and the directrix is y + 5 = 0.

A: Topic = Parabola As per guidelines, At a time only one question can be answered.

Q: What is the graph of the equation (x – xo)² + (y – yo)² + (z – zo)² = r² ? Sphere Cylinder Plane…

A: we have to cheek and find correct option

Q: Note: Enter your answer and show all the steps that you use to solve this problem in the space…

A:

Q: Q2) Let the equation of the circle is given as x² + y² + 2x – 4y – 11 = 0. Find the dis between the…

A:

Q: Q5/ Find the equation of the circle tangent to the lines y=2, x-3 and y = x+2.

A: Explained below

Q: Q2) Find the distance between the line y= - (x+2) & the center of the circle y+x-4(x+ y)= 9

A:

Q: Q2/ Find the equation of the circle tangent to the lines, y -2x+3, y = - 2x+7, y=+ and y =+

A: In the above question we have to find the equation of the circle at the tangents -  y= -2x+3 ; y =…

Q: 2. Sketch the graph of the cylinder given by 4x? + 9y² = 36.

A: Graph of the cylinder. You can assume that the the elliptical like shape is above the given figure…

Q: Q2) Find the distance between the line y= - (x+2 ) & the center of the circle y + x – 4(x+ y )= 9

A: The center of the circle x2+y2-2ax-2by+c=0 is a, b Therefore, the center of the given circle…

Q: Which of the following point (æ, y) on the graph of y = /2x is the nearest to the point (4,0) ?…

A: 1. The parametric form of equation Y2= 4aX is X = at2 and Y= 2at. 2. The perpendicular distance from…

Q: Q#01: Graph the vertical parabola for y= 2(x – 4)² – 3.

A: Given :              y = 2x-42 - 3 We will compare given equation with,                   x-h2 =…

Q: 10. Which equation represents the parabola that has been vertically stretched by a factor of 5,…

A:

Q: Find the equation of a line tangent to the circle x² + y² + 2x – 4y – 31 = 0 at the point (5,2).…

A: Given: The equation of the circle is  x2+y2+2x-4y-31=0   To determine: The equation of a line…

Q: Q2/ Find the equation of the circle tangent to the lines, y =-2x+3, y = - 2x+7, y-+늘and y- +글 %3D…

A: The lines given by y=-2x+3 and y=-2x+7 will be parallel to each other as they have the same slope m.…

Q: 1. Which is the equation of a parabola that is concave down with a y-intercept of 5? 1. y -+ 5x +1…

A:

Q: For what values of a and b is the line 4x + y = b tangent to the parabola y = ax² when x = 3? a = b…

A: Slope of the tangent is obtained by dy/dx

Q: - Find a parabola with equation y = ax? + bx +c that has slope 4 at x = 1, slope –8 at x = -1, and…

A:

Q: What are the new coordinates of A, on the graph below, after a reflection in the line y =x? 6. 4 B…

A: When reflecting a point across the line y = x, just switch the x and y coordinates

Q: 4. (The figure is NOT to scale!) T is the midpoint of line segment formed by U and X. What is x?…

A: Given query is to find the value kdu x and measure of UT and TX.

Q: The r coordinate of the point of intersection between the two curves y = e2" and y = 1 is a = (Write…

A: Solution let a  value x=xo is intersection point of two function ,say f(x) and g(x) which implies…

Q: To y=x²-12x + 20 Parabola Wite the intersection point of the tanpent lines drawn from (2,0) and…

A: Consider the given parabola and find the derivative of the parabola.…

Q: 7. Find the points of intersection of the following curves and draw the figure. x? – 3y = 0; x² + 2…

A: We have to solve these two equations to find intersection points of these two curves.

Q: Which of the following is the shortest distance from the point (5, 0) to the curve y = V2x ? a) 2 b)…

A:

Q: Find the x intercept(s) and the coordinates of the vertex for the parabola y = x^2 – 2x + 1. If…

A:

Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-2y=4?

A:

Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

A:

Q: 2. Find the point on the parabola x+y? 0 that is the closest to the point (0, -3).

A:

Q: Q1/ Find the equation of the circle tangent at least to three lines (y= 1, y= 5, x= 2 and x=7). 40%

A:

Q: 33) Find the points of intersection between the line x - y - 2 = 0 and the parabola y = 4 - x 2.

A: