3 On a separate piece of paper, sketch the graph of the parabola f(x) = x² + 6. axes, plot the point (0, –2). Notice that there are two points on the parabola [of t (a)) ] at which the tangent lines to the parabola pass through (0, –2). Draw thes iese two lines. bint with positive x-coordinate that is on the parabola and has its tangent line to th

Q: Tangents are drawn to the parabola y2 = 4ax at the point where the line Lx + my + n = 0 meets this…

A: Introduction:  A line that touches the parabola exactly at one point is called the tangent to a…

Q: The parabola y = x2 + C is to be tangent to the line y = x. Find C.

A: To find the value of C.

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: What is the family of curves for all parabolas with axes parallel to the y-axis.

A:

Q: A parabola is the locus of points equidistant from a given point (focus) and a line (directrix).…

A:

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: 1. Find all points P on the parabola y = x² such that the tangent line at P passes through the point…

A: Consider the given parabola, y=x2 and poiny 2,-5Find the derivative of the equation, dydx=ddxx2=2x

Q: 11. Find the equation of the line tangent to the parabola y=x²-3x+2 and perpendicular to the line…

A: Determine the equation of tangent line

Q: Find the equation of the osculating circle of the parabola y= 1 x' at the point where x = 1. Then 4.…

A: The given data is: The equation of a parabola is: y=12x2 To find the equation of the osculating…

Q: #62. Civil engineers often design road surfaces with parabolic cross sections to provide water…

A: Given: Width of the road (w) =32 feet radius of the road (r)=322=16 feet rise at center of road 0.4…

Q: 3. Find the equation of the tangent line to the parabola 4x² +9y² = 18z, x = 3 at the point (3, 2,…

A:

Q: 5. Figure Q5 shows the graph y = f(x) on the xy-plane. 54 -5- Figure Q5 (a) Does the graph above…

A:

Q: Write an equation for the parabola

A: Find the equation of parabola from the given data .

Q: 7. For whit value of b will the line y =- y 3x +4x -1? 2x+ b be tangent to the parabola

A:

Q: You will transform the basic (parent) quadratic relation y =x² . Your transformation needs to…

A:

Q: Find all points where the parabola y = 9 - x² 1 intersects the line y = zx+6. 2

A:

Q: For what values of a and b is the 2x + y =b  line tangent tothe parabola y =ax2 when x =2?

A: Rewrite the equation of the tangent line as y=-2x+b and its slope is -2.

Q: Find the focus of the parabola y = x 2 - 12x. (6, -35) (6.75, -36) (6, -35.75)

A: