4) Given :y = ax + bx +1, the curve touches the line x+ y = 0 at %3D The point (3,-3). Find the equation of the curve.

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: We have  y=ax2+bx+c        at (2,28)           and               y=4x

Q: 4. Find the equation for the line tangent to a. y=x²- 3 x + 5 at the point (2, 3)

A: We will find tangent equation.

Q: the sloper of the curve 2y2=ax2+b at (1,-1) is -1.Find a,b

A: 1) Find dydx at the given points to find the value of 'a' . 2) Now satisfy the point (1,-1) to the…

Q: 14. What is the slope of the curve at the point (0, x²+y-12r +4y = 5 %3D 0-2

A:

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: 5. Find an equation of the line tangent to the curve y = 3x² 1 and parallel to the line 2x – y + 3 =…

A: Explained below

Q: Find an equation of the tangent line to the graph 16x4 + y4 = 32 at the point (1,2). %3D 1) 5 1 -+x-…

A:

Q: Find the equation of the curve that passes through the point (7,5) if its slope is given by dy 3D 8х…

A: We have to find

Q: the slope of the curve 2y2=ax2+b at (1,-1) is -1.Find a,b

A:

Q: Find an equation of the curve that passes through the point (1, 3), and has the given slope y′ =…

A:

Q: The slope of the tangent line to the parabola y = 2x + 5x + 7 at the point (- 4, 19) is: The…

A:

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A:

Q: Find the point where the line tangent to y=x* – 3x² +2 at (2, 6) crosses the x – axis.

A: y=x4-3x2+2,  2, 6 Differentiating with respect to x, we get dydx=4x3-32x+0=4x3-6x Now slope of the…

Q: the slope of the curve 2y2=ax2+b at (1,-1) is -1.find a,b

A: The equation of the curve is  2y2 = ax2+b…

Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

A:

Q: Find a parabola with equation y = ax² + bx + c that has slope 4 at x = 1, slope -16 at x = -1, and…

A: We know slope of a curve y=f(x) is given by, dydx=f'(x)

Q: Find an equation of the curve that passes through the point (0, -7) and whose slope at the point 2x…

A: we have to find the equation of the curve

Q: Find equations of both lines through the point (2, - 3) that are tangent to the parabola y = x2  + x…

A:

Q: Find the equation of the curve that passes through the point (6, 6) if its slope is given by dy = 7x…

A:

Q: The slope of the curve 2x + Vx + y = y at the point (0, 1) is

A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

Q: The point on the curve y=vx+2 which is closest to the point (5,2) is

A:

Q: Find an equation of the curve that passes through the point (3, 1), and has the given slope y′ = −…

A: Given that y'=-y5xdydx=-y5x

Q: Y = ce" || if the angles of the intersection are 7 radians.

A:

Q: 10. Find the slope-intercept form of the equation of the line tangent to the graph of y arctan(9x)…

A: Given y = arc tan9xand x=39here we find the slope - intercept form of the equation of the line…

Q: Find the slope of the curve y = 2x(x-1)° at point (1,-1). %3D O -1 O 4 O 2 O -2 O 1

A:

Q: 2.) What is the equation of the line tangent to y(x) x- 2r3+6x-3 at r =-1?

A: Follow the steps .

Q: Find the equation of the curve that passes through the point (3, 2) if its slope is given by y = dy…

A:

Q: 2) Find the equation of the curve whose slope at any point p(x,y) is m =x (x +5)² and passing…

A:

Q: (b) the curve x = = y²-y-6 and the line x = = 2y + 4;

A: Given; x=y^2-y-6, x=2y+4

Q: 4. Find the equation for the line tangent to a. y= x²- 3 x + 5 at the point (2, 3)

A:

Q: Find the equation of the family of curves whose slope at any point (x,y) is given and which passes…

A:

Q: Find an equation of the curve that passes through the point (0, 2), and has the given slope y′ =…

A: y'=x4y, (0,2) Formula ∫xndx=xn+1n+1+C

Q: Show that the solution of the equation YUx – xUy = 0 containing the curve x² + y² = a², u= y, does…

A: Given that y ux – x uy = 0, The Lagrange’s auxiliary equation for the given equation is given as:…

Q: What is the equation of the line tangent to the curvev= x² – 1 at the point -2,3) y = x+ O y=-4x +…

A:

Q: Sketch the curve y = x/(x² – 9). Enumerate the steps in your solution.

A: as per our guidelines, we are supposed to answer only one question if there are multiple questions…

Q: Find an equation of the curve that passes through the point (1, 1), and has the given slope y′ = −…

A: y'=-9x16yPasses through (1,1)Formula∫xndx=xn+1n+1+C

Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

A:

Q: The line y = 3x+7 and the curve xy-x = 4 intersects at the points A and B Show that the equation to…

A: Given Data: Equation of the line: y=3x+7 ......(1) Equation of the curve: xy-x2=4 ......(2) The line…

Q: Find the point on the curve y = √x closest to the point (2,2)

A: Here we have to find the point on the curve y = sqrt (x) closest to the point (2, 2)   use the…

Q: Find an equation of the curve that passes through the point (0,1) and whose slope at (x, y) is 11xy

A:

Q: find an equation of a straight line tangent to the curve y=e^x and passing (0,0).

A:

Q: Find the equation of the line tangent to the curve y =8/x2+4 at the point (2, 1).

A:

Q: The slope of the curve y^2-xy-3x=1 at the point (0,-1)

A:

Q: Find the point on the graph y=Vx+1 that is closest to the point (2, 1).

A:

Q: The equation of the tangent to the curve y = x – 3x² – 2x + 2 at the point where the curve cuts the…

A: We have to find  the equation of tangent in the form of y=mx+c.

Q: Find an equation of the curve that passes through thepoint (0, 1)and whose slope at (x, y) is xy.

A: To Determine: Find an equation of the curve that passes through the point (0, 1)and whose slope at…

Q: 17. The line with equation y = 2x b where bis a constant, passes through the point (3, 6). What is…

A: When a line passes through a point then the coordinate  values of the point must satisfy the…

Q: A curve C has equation y =x2lnx- 2x +5, x > 0. %3D For which values of x, the curve C is convex?

A: The equation of the given curve is  y=13x2 ln x-2x+5 , x&gt;0 For the curve to be convex its second…

Q: Two objects moving along x-axis are starting at the same time. Their positions are measured in…

A: Given the equation of the motion of the object 1 and object 2 are s1 = 2t2 - 3t , s2 = 3t - t2

Q: 4) Find the slope of the curve y = 3x + 1 at point P (1,2)

A: We need to find slope of curve at given point.