Identify the curve represented by the equation 21x² +21y² – 24xy= - 3 from the options below. O1. Hyperbola. O II. The equation has no graph. O II. Ellipse.

Q: Q 03: find the orthogonal trajectory of family of parabolas represented by the equation y? = 4ax…

A: Given y2 = 4ax2y dydx = 4adydx = 4a2ya = 2yy'4= yy'2y2 = 2xy dydx

Q: Which graph represents the following ellipse x^2/81+y^2/9=1?

A: The equation of ellipse is x281+y29=1.

Q: find a cartesian equation for the curve r2 = 14

A: Find a cartesian equation for the curve         r2 = 14

Q: 6. What is the equation of the ellipse whose graph is shown below? (1,4) (7. 0) C(1,0) (4, -54 3 A)…

A: Graph of the ellipse is given, we have to find its equation

Q: Find the equation of the parabola, y = ax^2 + bx + c, that passes through the points (0,5), (2,-5),…

A: we have to find the equation of the parabola y=ax2+bx+c that passes through the points (0,5), (2,-5)…

Q: 4. Find the focus, directrix and vertex of the parabola (x + 2)2 = 3y - 6, then sketch the curve.

A:

Q: Find the equation of the asymptote with a positive slope for the following hyperbola. (x + 8)? 1 (y…

A: Given hyperbola s standard equation of hyperbola : Therefore,

Q: (b) Find an equation for the parabola that has axis x = -1 and passes [3] through the points (4,5)…

A: Directrix is a line which together with a point called the focus defines the set of points that form…

Q: Hx'+y°-4x+Dy = - 2

A: This question is based on formation of perfect square and solving inequality notation.

Q: What is the equation of the ellipse shown in the graph? y 67 +►X -10 8 -6 -4 -2 0 -2+ 2 4 6 8 10 -44…

A: Major axis: The longest diameter of an ellipse is known as the major axis. It extends from one side…

Q: 2. Sketch and identify the graph of the equation a + y? – 2y –- 3 = 0 in 3D.

A: x2+y2-2y-3=0x2+y2-2y+1-4=0x2+(y-1)2=4The equation represents circle in 2D,but a cylinder of radius 2…

Q: Graph the given ellipse 22 9 + y² 4 1.

A: given equationx29+y24=1

Q: Find an equation for the indicated half of the parabola.Lower half of (y + 1)2 = x + 3

A: Given equation is y+12=x+3.

Q: (x – 6)? (y – 4)? = 1 Given the ellipse 4 25 Find the center point: (6,4) List the four vertices:

A:

Q: Find the equation of the parabola, y=ax^2 + bx + c, that passes through the points (1,4), (-1,0),…

A:

Q: find the equation of the parabola y = ax? + bx + c that passes through the points. (0, 3), (1, 4),…

A:

Q: 16. Which equation represents a parabola with vertex (4, 4) and directrix y = 2? O y = 2a2 - 4x + 4…

A: We need to find the equation of parabola whose vertex is (4,4) and directrix is y = 2

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

A:

Q: (d) If x + y = xy, show that y" = . (e) Evaluate y" for the ellipse b'x? + a²y² = a²b°.

A: We have to differentiate the given expressions with respect to x.

Q: Determine the graph of the second degree equation x? + y² – 6y + 2x + 10 = 0. NONE OF THESE…

A: We have to choose option

Q: 2x2 + 3y2 – 12 = 0 - 24 1 44 200 12 14 14 15 14 24 erom 22 24 24 O y=vC(12-2x*2)/3) O…

A:

Q: Find the equation of the parabola y = ax? + bx + c passing through the points (0, 6), (- 2, 2), and…

A:

Q: Determine the relation of the ellipse x + 4y° = 32 and the line 2x +y-1 0.

A: To Determine: the relation between the ellipse x2+4y2=32 and the line 2x+y-1=0 Given: we have two…

Q: Graph the given ellipse. (x – 4)² + (y – 2) = 1 16 6.

A: Given,  (x-4)216+(y-2)29=1

Q: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

A:

Q: Which graph represents the following ellipse (z+1)ª + 16 (v-3)° 36 = 1?

A:

Q: Find the point on the parabola y = (x – 3)² – 5 that is closest to the point (0,0). |

A:

Q: Determine the relation of the ellipse x + 4y = 32 and the line 2x +y-1 0.

A: Step:-1 Given conic and line is x2 +4y2 =32   and 2x+y-1=0 To find the relation between the ellipse…

Q: Determine the equation of the directrix of the curve 3x=2y2-4y+7 (Graph Solution) a. x=30/20…

A:

Q: 10) For the equation of ellipse below, find the distance between vertices. * 4(y + 1)? + 7(x – 1)? =…

A: Distance between vertex is 2a. Where a is semi-major axis.    Answer : Option a. 2√7

Q: Find the points on the ellipse x^2 + 9y^2 = 9 and the line x + y = 10 that are closest and farthest…

A: Distance between the two points: - The length of the line segment connecting two places is called…

Q: 5. Put the following equation into standard form, classify it as a circle, ellipse, hyperbola, or…

A:

Q: [24] Complete the square to determine the type of curve represented by the equation: 4x +9y² –16x–…

A: The given question is taken from the conic section in which we have to find out the given equation…

Q: Find a Cartesian equation for the curve and identify it as either a hyperbola, circle, limaAson,…

A:

Q: Find equations for the osculating circles of the parabola y=0.5x2 at the points (0,0) and (-1,1/2).

A:

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

A:

Q: Graph the parabola. y=x y3x+10x+21 Plot five points on the parabola: the vertex, two points to the…

A: See the details solution in below

Q: Graph the parabola y2 - 2x - 2y - 5 = 0. Give the location of the focus and the directrix.

A: We have to graph the parabola and we have to give the location of the focus and the directrix where…

Q: For the Ellipse x?+4y -16 x-24 y = -19 Find the following:

A:

Q: Find equations for two lines through the origin that are tangent to the ellipse x - 8x + y² + 5 = 0.

A:

Q: Which are the foci for the hyperbola modeled by the equation (Y-32 (x-1)² _ -1? 36 13

A:

Q: Find the equation of the major axis of the ellipse x? +4 y? - 6 x - 24 y = -36 Select one: O y= 0 O…

A: First of all we will write the equation of ellipse in standard form.

Q: d. Find the equation of the vertical parabola that passes through the points: A = (6, 1), B = (-2,…

A:

Q: Find the equation for the parabola that has its focus at (-53/4, -7) and has directrix x = 5/4.

A:

Q: Find the equation of the parabola y = ax^2 + bx +c that passes through the points (-1,-4) (1,4), and…

A: topic  -  parabola

Q: Find the slope of the ellipse x^2 + 4y^2-10x- 16y +5=0 at the point where y=2+ 8 0.5 and x-7* O…

A: Given equation of the ellipse is as following: x2+4y2-10x-16y+5=0. We know that the slope of an…

Q: Find the coefficients a, b, c, and d so that the curve 20 shown in the accompanying figure is the…

A: Given y = ax3+bx2+cx+d                           (1) The point (0,10) satisfies the equation (1) ,…

Q: 4. What is the focus of the parabola whose equation is -(y- 3)2 = (x – 2)? O A. (2, 1) OB. (0, 3)…

A:

Q: What is the distance between the vertices of the ellipse: 64x^2 + 25y^2 _ 16x - 16y-648= = 0? C.…

A: