4 Find a. the equations of the tangents to the circle x'+y +4x-2y-24 0 at the points where the circle cuts the line y =x. b. the length of the tangents from the point (2, 5) to the circle x + y -14x - 2y +34 = 0

Q: 12) Circle O is tangent to L: 5x - 12y + 19 = 0 and L 5x 12y 7=0. If the center of the Circle O is…

A: The given tangent lines are, L1: 5x - 12y + 19 = 0L2: 5x - 2y - 7 = 0both lines are in the form ax +…

Q: 23. The line 3x - 4y + 14 is a tangent to the circle

A: 23 Given equation of tangent is 3x-4y+14. General equation of circle is x2+y2+2gx+2fy+c=0 radius of…

Q: 2 Find an equation of the line L, where L is perpendicular to y =x and passes through the point…

A: Given a Line L which is perpendicular to  y = (2/3)x  at point (3,2)  Equation of line L is…

Q: 20. The tangent of the acute angle between the y= 4x-3 and y=x-5 is 2 (A) 5 [B) [C) 3 (DJ The radius…

A: tan(θ)=m1-m2/1+m1m2

Q: Suppose a curve is defined by the equation 16(x² + y²) = 45. Show that if you translate the curve to…

A: we have to translate the curve.

Q: nd the equation of the tangent to the circle X^2+Y^2-8X+2Y+7=0 at point (3,2), given that point…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2.1 Identify and sketch the graph of y = /9 – 4x². Show all the necessary points on the curve and…

A: We can square the left-hand side and right-hand side then we get y2 = 9-4x2

Q: 3. Consider the circle C given by the equation x² + y² – 8x + 4y – 12 = 0. Give the point-slope form…

A: we have to determine the point slope form

Q: Find the exact length of the curve.

A:

Q: 2 Find the distance from the point B = [0 5 0 to the line 1 +t| 0 -3

A: Here we will find the distance between the given point and line,

Q: Find equation of the circle ( in general form ) that satisfies the given condition. 11. Equation of…

A: This question is based on conic section.

Q: Find the exact length of the curve. y = 1 - e-x ,    0≤   x ≤ 2

A:

Q: Find the coordinates of the point on the graph of y = x^2− x + 3 at which the tangent is parallel to…

A:

Q: 6. Determine the equation of the circle whose center is at (4, 5) and tangent to the circle whose…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the distance from the point Q to the line ℓ. Q = (2, 2), ℓ with equation [x y] = [-1 3] + t [1…

A: GIVEN: Q = (2,2)               xy = -13 + t 1-1

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

A:

Q: Suppose we follow Sir Isaac Barrow's method of finding the tangent implicitly for the circle with…

A: given equation of circle  x2+y2=9 using Sir Isaac Barrow's method and replace x,y→x-e, y-a equation…

Q: Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6,5) ||…

A:

Q: Find the length of the curve with equation x2 (y + 1)3 from the point where æ = 0 to the point where…

A: Since the given curve is  x2=y+13      from point x=0 to x=33. Given curve can be written as x=y+132…

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

A:

Q: 9. Find the point of intersection of the two curves, * y = 2r-1 y = x-2r O(-) none of these

A: To find out the point of intersection of curves.

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: A line meets a curve y=2x-1 at the point (5,4). The line is tangent to the circde C:x +y² +10x+8y+…

A:

Q: Find the values of a and b for the curve x2y + ay? = b if the point (1,1) is on its graph and the…

A: The slope of the tangent 'm' at a point (x1,y1) for a curve S(x,y) Is given by dydxx1,y1 therefore…

Q: 1. Find the standard form of the equation of the circle tangent to both axes at (-3,0) and (0,3).

A:

Q: Find the values of a and b for the curve x2y +ay? -b if the point (2, 2) is on its graph and the…

A: Given x2y+ay2=b

Q: Find the tangent lines as directed. To the parabola y=6x-3 perpendicular to the line x+3y=7

A:

Q: Find an equation of the tangent line to the graph at the given point.

A: The equation of the given graph: x23+y23=5

Q: Prove that the curves y2 = 4x and y2-6x+1 = 0 touch each other at the point (1,2)

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: Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)

A:

Q: 2. Find the equation of the line that is tangent to the circle x + y = 25 at the point P(3,4)

A:

Q: Find the length of the tangent to the circle x²+y²-2x-3y-1=0 from the point (2,5).

A:

Q: 4. Find the two values of a for which the line connecting the point (1, –1) to a point (a, a²) on…

A:

Q: 29.Consider the circle (x + 1)² + (y – 3)² = 116. Find an equation for the tangent line drawn to the…

A: Since you have asked multiple unrelated questions in a single request we would be answering only the…

Q: Find the exact length of the curve y = (2/3)(x^2-1)^(3/2), where 1 is less than or equal to x which…

A:

Q: Find the values of a and b for the curve x2 y + ay2= b if the point (1,1) is on its graph and the…

A: Find the slope of tangent line

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

A: Topic = application of derivatives

Q: 1 + 12 8x*' - Find the length of the curve y= 1<x<2. 4

A: y=x612+18x4 Differentiate the  above equation dydx=ddxx612+18x4dydx=x52-121x5

Q: Find equations for the tangents to the circle (x - 2)2 + ( y - 1)2 = 5 at the points where the…

A:

Q: Find the equation of the circle tangent to the line 3x- 4y+ 6 = 0 at (2,3) and passing through (-1,…

A:

Q: 2. Consider the curve given by 3y2 – 2x²y³ +2x +9 = 0. Write an equation for the tangent line to…

A: The given curve is, 3y2-2x2y3+2x+9=0 The slope of the tangent curve is given by dydx Determine the…

Q: Find the values of a and b for the curve x²y+ay²=b if the point (1,1) is on its graph and the…

A: It is given that, x2y+ay2=b   ...(1)and4x+3y=7    ...(2) Here equation 2 represent a tangent line…

Q: 6. Show that if m is any real number, then there are exactly two lines of slope m that are tangent…

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: Given,  (a) Equation of the circle   x2+y2+4x-2y-24 = 0  We have to find the equations of tangents…

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: . Verify that the given point lies on the curve. p. Determine an equation of the line tangent to the…

A: given  point (2,1)

Q: 4 The line y= -Lx+3 has a perpendicu lar which fangent to the graph of y= (x²-2) (2x+k) at x=-l,…

A: