Q2) Find the equation of the tangent to the hyperbola x? – 3y² = 1 at the point S(2,-1). %3D A) 2x + 3y – 1= 0 B) 3x + 2y – 1 = 0 С) х — Зу- 2 %3 0 D) 2x – 3y = 0 E) х — Зу %3D 1

Q: (x − 6)²(y+3)² + 36 25 = 1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: S52² +32° +22²-32 +2) dz

A: Solving the problem by finding the value of integration.

Q: Determine the roots of y"" - 4y" + 3y = 0

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Q: What is the general equation of a parabola that opens upward with V(-1,2)?

A: The general equation of the parabola opening upwards is x-h2=4py-k where (h,k) is vertex. here…

Q: Derive the equation of the parabola with a focus at (2, 4) and a directrix of y = 8. 1 O f(x) -(x –…

A: Given query is to find the equation of parabola.

Q: 13. Which of the following is the equation of the graph shown? 2 Parabola Oy = - 3x? – 6x – 2 Oy = -…

A: The objective is to find the equation of the graph.

Q: 3. Find the points of intersection of the parabola ²-4x+y=0 and the line-2x+y=-3

A: Let the co-ordinate of the intersection point be (x, y).  Then (x, y) lies both on the parabola and…

Q: Find the value of Y for the hyperbola defined by the equation y² – x² = 7 at the point (3, 4). dx2

A: The equation is y2-x2=7. First find the value of dydx as follows.…

Q: 5 Find an equation of the hyperbola having foci at (-2, - 3-/29) and (-2, – 3+ /29) and asymptotes…

A:

Q: Find the point on the hyperbola x²-9y² 9 where the line 5x + 12y = 9 touches it.

A: Solving                  5x+12y=9  or            y=9-5x12   and   x2-9y2=9  We have…

Q: 7. A parabola whose equation is y =r² - 2x + k has a turning point with coordinates (1,-5). Find the…

A: We have to find k

Q: 2 Write the equation of the hyperbola – 25 · x? + 16 · y² = 400 in standard form + = 1 %3D

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Q: Find mzV. V W (2x + 29) (10x- 27)° Y

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: For which values of a does the conic 3x^2 + 2y^2 − 16y + 12x =a, have at least one point?

A: Consider the given:…

Q: What is the equation of the parabola that opens to the right and with vertex at (4,-2) and a latus…

A: Prabola

Q: Standardize the conic with the equation 7x2+4xy+4y2--2x-6y+1=0

A:

Q: y -1 Q2) L, =Xx2 = -1 - 2 Fand equation of plane Canternng them

A:

Q: -4, 0) Ay \ 2x (1, 0) -2 -2 (-1, 0) 4 (4, 0) 6' -3 1. 1 3 x 4 (2, 0) (-2, 0) 5. 4, 0) 4 2 6.

A: We have to find the intercepts of the x axis of the equation of the given graphs.

Q: The equation of the parabola y' = 4ax is in the standard form. FALSE O TRUE

A: The given equation of parabola is -  y2 = 4ax

Q: Let r, r, and r, be the roots of x’ +3x² –5x-4=0, construct the equation whose roots are: 7 (r, +r,…

A:

Q: The orthogonal trajectory of y = ce* is a parabola of the form y = ax+b. Find the values of a & b so…

A: We are asked to find the value of a and b

Q: nd the equation of the parabola with vertex at (5,-2) and focus at (5,-4). (x – 5)² = 8(y + 2) (x +…

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Q: The equation of the line touching both the parabolas y = 4x and x' =-32y is x-2y+1 = 0, then a is

A: Introduction :

Q: find the key values for a conic a. y^2 - 8x - 4y + 4 = 0   b. 6x^2 - 4y^2 -12x-8y-22=0   c. x^2…

A: a y2-8x-4y+4=0y2-4y+4-8x=0y-22=8xwhere y=y-2 , a=2which is the general form of a parabolavertex…