D. Find the equations of tangent to circle x +y 2 -16x -12y +87 = 0 at y = 4 (Write the equation of the line in y = mx +b form).

Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0≤t≤2

A:

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

A: Answer

Q: Sketch the curve (2² + y*)³ = 4.x²y? 2.2

A: To sketch the graph of:(x2+y2)3=4x2y2

Q: For what values of a and b is the line 5x + y = b tangent to the parabola y = ax? when x = 4?

A: y=ax2y'=2axy'(4)=2a(4)y'(4)=8a Now we have 5x+y=b ⇒y=-5x+b Compare with the equation y=mx+b From…

Q: Explain the steps required to find the length of a curve y = ƒ1x2 between x = a and x = b.

A:

Q: Find the equation of the family of curves whose at any point (X, Y) is 1. 3x? + 4 2. * y X+1 3. y-1…

A: Here, there is a little word missing in sentence, 'Find the equation of family of curves whose slope…

Q: Find the equation of the line tangent to the circle x + y + 6x - 2y - 15 = 0 at the point (1,-2).

A:

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

A:

Q: The surface of a mountain is modeled by the equation h(x, y) = 7000 - 0.001x2 - 0.004y2. A mountain…

A:

Q: finel the equation of the line Hhetis taugent y= y% 2X at x =2

A:

Q: (d) Find the points on the curve x'y = 60 nearest the origin.

A:

Q: Find the equation of the circle if the circle is tangent to the line x + y = 1 at the point (0,1)…

A:

Q: Find an equation of the line which is tangent to the circle z + y - 4x + 6y – 12 = 0 at the point…

A:

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

A:

Q: 2* + y – 10x+ 18y – 90 = 0 is the equation of a circle with center (h, k) and radius r for:

A: The given equation of a circle x2+y2-10x+18y-90=0 Completing the squares…

Q: Find the points on the curve y = 14x closest to the point (0, 1). and

A: This question is based on application of Derivative.

Q: - Find the equation of the tangent to the circle x2 С. Зх + 5y + D. Зx - 5y + А. Зх + 5y -34%3D0 B.…

A: Find the equation of the tangent to the circle x² + y2 - 34 = 0 through (3, 5).

Q: Write the equation of the line tangent to the curve x In y+7xy = 28 at the point (4, 1). 32 y-7x 60…

A:

Q: Find the equation of the circle tangent to 3x+y+14=0 and x+3y+10=0 with radius square root of 10

A: A tangent to a circle is perpendicular to the radius vector on the point of contact. To find the…

Q: Find equations for two lines through the origin that are tangent to the ellipse x2 – 8x + y² + 3 =…

A:

Q: 4 Find a. the equations of the tangents to the circle x + y? +4x-2y-24 = 0 at the points where the…

A: 4(a). The given equation of circle is: x2+y2+4x-2y-24=0

Q: 6. Show that the line with equation y = 3x – 5 is a tangent to the circle with equation x² +y? + 2x…

A: Equation of line : y=3x-5 Equation of circle : x2 + y2 +2x -4y -5=0 We have to prove that the line…

Q: 4 Find a. the equations of the tangents to the circle x +y + 4x – 2y – 24 = 0 at the points where…

A:

Q: Find the lines tangent to the ellipse x2/4 + y2/9=1 that contain the point (4, 0).

A: We at first consider the equation of tangent  to x2/4 + y2 /9=1 with slope m. Then we find the value…

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: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

A:

Q: Eliminate the parameter to find a Cartesian equation of the curve. x = t2,    y = t5

A: A curve is a two-dimensional object with equation of the form y=f(x). Curves can be parameterized to…

Q: Find the equation of the circle, if the center of the circle of radius 3 lies on the line x + 2y = 4…

A: Let the center of the circle is (h, k). If its center passing through the line x + 2y = 4, then h+…

Q: Find the midpoint of the line segment joining the points P1 and P2 . Equation: y3 = x + 1Points: (1,…

A: Given y3=x+1 Points: (1, 2); (0, 1); ( - 1, 0)

Q: The curves x=y²and x = 2 y – y?

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: b. the length of the tangents from the point (2, 5) to the circle x +y² -14x-2y+34= 0

A:

Q: Find the exact length of the curve. y = 5 + 8x/2, 0<x<1

A: Topic = application of derivatives

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

A: Consider the equation of the parabola, y=ax2 differentiate the equation with respect to x to find…

Q: Find the equation of the line tangent to the circle expressed as x^2 + y^2=5 at the point (x,y)=…

A: The equation of tangent to a circle S at the point (x1,y1) is given by the formula S1. Where S: is…

Q: What is the standard equation of the circle center at (3, 4) and tangent to the line x + 2y = 1? A.…

A:

Q: Find equations for two lines through the origin that are tangent to the ellipse x – 4.x + y² + 3 =…

A:

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

A:

Q: At what points will the line y = -2x intersect the unit circle x2 +y2 =1 ?

A: The circle equation is x2+y2=1 and the line equation is y=-2x.

Q: Find the equation/s of the circle that has a radius of 5 and tangent to the  line 3x + 4y − 24 = 0…

A: The solution is given below

Q: Find equations for two lines through the origin that are tangent to the ellipse x? – 4x + y? + 3 =…

A: Solve for the equation

Q: How far from the x-axis is the center of the curve 2x2 – 2y2 + 10x – 6y – 55 = 0?

A: The given equation of the curve is: 2x2 – 2y2 + 10x – 6y – 55 = 0 This can be written as:

Q: 27. The equation of the common tangent to the circles x+ y - 12x- 2y-123D0 and x*+y - 4x + 4y + 4 0…

A: Note: "Since you have asked multiple questions, we will solve the first question asked by you. If…

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: Write an equation of the line that is tangent to the circle at the given point. (x – 2)2 + (y+ 7)² =…

A: The tangent of the curve is the line that touches the curve at only one point and the tangent of a…

Q: For what values of aa and bb is the line −4x+y=b-4x+y=b tangent to the curve y=ax2y=ax2 when…

A:

Q: The length of the curve 4/2 3 y = xi - 1,0 < x < 1 is .

A: Given,            The length of the curve y=423x32-1 , 0≤x≤1 is 136.To find : Check whether the…

Q: 2. Find the equation of the tangent to the circle x2 + y2 +4x +16y - 32 = 0 through (4, 0).

A:

Q: What is an equation of a circle whose center is at (2, -4) and is tangent to the line x = -2? Select…

A: