A point moves on the parabola 10y = 5x² + 3 in such a way that when x = 6, the abscissa is increasing at the rate of 2 ft per second. At what rate is the ordinary increasing at that point?

Q: Find the tangent to the parabola (x + 2y)² + 2x - y - 3 = 0, parallel to the line x - y = 1.

A: Consider the equation of the line x-y=1 ⇒y=x -1 Comparing with y=mx+c we get slope of line, m=1

Q: The focus of the parabola y^2 = 4x is at

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Q: raveling due north at 570 mi/hr. Assuming both airliners maintain their (equal) elevations, how fast…

A: In this question, the concept of the derivative is applied to calculate the rate of change.…

Q: Find the coordinates of the point on the parabola y = x² which is closest to the point (3, 0).

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Q: Find the equation of a parabola whose latus rectum is joined by points (2, 1) and (-4, 1)

A: Use equation of parabola

Q: Aaron tosses a stone into a still pond, producing ripples shaped like concentric circles. One of the…

A: Here we have to use the concept of derivatives.

Q: For the parabola y=-4(x+1)^2 - 3, the range is...?

A: For  y=ax2+bx+c  with vertex      (x1  y1)

Q: What is the effect on the graph of a parabola if it's equation in standard form has increasing value…

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Q: If the parabola y=x^2+C is tangent to the line y=4x+3, find the value of C. a. 5 b. 6 c. 6

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Q: Q,9. What point on the parabola y = v2x + 5 comes closest to the ori

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Q: Find the standard equation of a parabola if its latus rectum measures 9 units, axis at y = 3, p is…

A: Let's find standard equation of a parabola.

Q: 5. Show that the sum of the intercepts of the tangent to the parabola (Art. 129), x+y=a¹, is equal…

A: We need to prove given theorem.

Q: Find a quadratic function with a root at X 5i that also includes the point (2, 14).

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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.