The condition that the parabolas y? = 4ax and y² = 4c(x – b) %3D have a common normal other than x axis (a, b, c being distinct positive real numbers) is b < 2 (A) а -с (В) > 2 а -с (C) < 1 (D) > 1

Q: Prove that for any point (a, b) ≠ (0, 0) on the parabola y = x2 , the normal line intersects the…

A: The given equation of parabola is y=x2  For the point (a,b)≠ (0, 0), the slope of normal is and at…

Q: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: teps that it took to convert to that form.. (9) fix,y) = X ty+xy i

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Q: The stationary points of ymx³+4x²-3x+2 are ( decimal places ) and ( Type your answer to 2

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Q: 11) Find each of the two areas bounded by the curves y=x3-4x and y=x² + 2x Points of intersection:…

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Q: 3. Find the points of intersection of the parabola ²-4x+y=0 and the line-2x+y=-3

A: Let the co-ordinate of the intersection point be (x, y).  Then (x, y) lies both on the parabola and…

Q: For the given data (0, 5), (1,9), (4, 3) find the curve y = a + byx that best fits the data in the…

A: Given the data (0, 5), (1, 9), (4, 3)

Q: 1. y = - V2x +1 2. y = (x – 1)3 + 2 3. y =-1 2x 4. y? = 6– x 5. y = 1- |x|

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Q: Use Lagrange quadratic polynomial to estimate the value of y at x = 1.5 from the data points (0,…

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Q: Use least-squares regression to fit a straight line y = f(x) = Ax+B  to:   xi -8 -3 0 4 6 yi 7 4 2…

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Q: Find two positive numbers whose product is a such that their sum is minimum.

A: Let the two numbers are x and y So, xy=a y=a/x   Their sum= S= x+y We have to minimize S

Q: When X and Y are moving in the same direction the cross-products are likely to be

A: Cross Product :  It is a vector operation that acts on vectors in three dimensions and results in…

Q: For the given data (0, 1), (1, 1), (2, 3), (3, 5) find the line y = ao + a1x that best fits the data…

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Q: Find the orthogonal trajectories of the family of 2 curves x² + y² = cy A B Ⓒ с D none of the…

A: Given curve x2+y2=cy

Q: Find the point(s) on the line y = 7x + 3 closest to the point (−1, 8).

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Q: The points at which the graph of the equation 8x2+ y² – 16x + 8y + 8=0 has horizontal tangent lines…

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Q: Determine the distance from the line y = x + 1 to the parabola y2 = x. (Hint: Let (x, y) be a point…

A: The shortest distance from the line y = x + 1 to the parabola y2=x. Equation of line y = x + 1is…

Q: Find all zeros of f(x) = a + 4x² + x + 4. Enter the zeros separated by commas.

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