y = x2
y' = 2x (the slope of the tangent line at a point on the curve of y = x2)
Since the graph of the given equation it is a parabola (which has the y-axis as a line of symmetry), let's evaluate the slope of the tangent lines l1 and l2 that pass through the points (-3, 9) and (3, 9).
So that
m1 = 2(-3) = -6
m2 = 2(3) = 6
Use those slopes and the points (-3, 9) and (3, 9) to find the equations of the tangent lines such that
For l1:
(y - 9) = -6(x - -3)
y - 9 = -6x - 18
y = -6x - 9
For l2:
(y - 9) = 6(x - 3)
y - 9 = 6x - 18
y = 6x - 9
Now we have to find the intersection point of the two tangents.
y = -6x - 9
y = 6x - 9 (add both equations)
0 = -12x
0 = x yields y = -9
Thus, the intersection point of the two tangents of the graph of y = x2 at points (-3, 9) and (3, 9) is (0, -9).
Two curves which intersect at right angles, ( the angle between the two tangents to the curve) curves at the point of intersection are called orthogonal trajectories. The product of the slopes of the two tangents is -1.
To measure the point at which two tangents intersect each other, find an equation for each tangent line and compute the intersection. The tangent is the slope of a curve at a point. Knowing that slope and the coordinates of that point, you can determine the equation of the tangent line using one of the forms of a line such as point-slope, point-point, point-intercept, etc. Do the same for the other tangent. Solve the two equations as a system of two equations in two unknowns and you will have the point of intersection.
Tangent to the curve.
There are infinitely many points on the curve defined by the equation so it is not possible to list them.
The point with the given coordinates does not lie on the curve and so the question makes no sense.
Two curves which intersect at right angles, ( the angle between the two tangents to the curve) curves at the point of intersection are called orthogonal trajectories. The product of the slopes of the two tangents is -1.
The gradient of the tangents to the curve.
To measure the point at which two tangents intersect each other, find an equation for each tangent line and compute the intersection. The tangent is the slope of a curve at a point. Knowing that slope and the coordinates of that point, you can determine the equation of the tangent line using one of the forms of a line such as point-slope, point-point, point-intercept, etc. Do the same for the other tangent. Solve the two equations as a system of two equations in two unknowns and you will have the point of intersection.
If you mean the coordinates of the line x-y = 2 that intersects the curve of x2-4y2 = 5 Then the coordinates work out as: (3, 1) and (7/3, 1/3)
Two tangents can be drawn from a point outside a circle to the circle. The answer for other curves depends on the curve.
Where the demand curve and supply curve intersect.
Tangent to the curve.
by finding where the supply curve and the demand curve intersect
of average product.
No
Curve line?
There are infinitely many points on the curve defined by the equation so it is not possible to list them.