Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D OA(-눈-)and () (주·주) pue OB. (-V7, V7) and (v7, -V7) Oc. (0, ±1) OD. (tV7,0)

Q: A) Find the nearest distance from the point (-4,2) and the line 2x-y =5 B) Find and tx sin 3z and y…

A: We use derivatives application to find minimize distance from a point to a line

Q: Q5) Find the coefficients a, b, c and d such that the curve defined by; y = ax³ + bx² + cx + d,…

A: Given: The curve y=ax3+bx2+cx+d passes through the points 0, 10, 1, 7, 3, -11, 4, -14. To find: The…

Q: Create a 3-D plot of the function sin(/x² + y²) Vx² + y² for -8 <x5 8 and –8 < x < 8.

A: Note: Here, we are considering -8 ≤ x ≤ 8 and -8 ≤ y ≤ 8 rather than -8 ≤ x ≤ 8 and -8 ≤ x ≤ 8. We…

Q: Find the angle between the lines y-V3x-5=0 and 3y-x+6=0. %3D

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Q: y=csinx  Identify the curves that intersect the curves under a right angle.

A: Given- y = c sinx To find- Identify the curves that intersect the curves under a right angle.

Q: Q5) Find the coefficients a, b,c and d such that the curve defined by; y = ax3 + bx² + cx + d,…

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Q: Q4/ Find the angle between the curves x² = y & y² = x

A: The curves intersect at (1,1).  Now calculate slope at (1,1):  ddxx21,1=ddxy1,12x1,1=dydx1,1m1=2…

Q: Estimate f(2.06, 3.91) assuming that f(2,4)= 5, fx(2, 4) = 0.3, (Use decimal notation. Give your…

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Q: For the curve 2² - 4xy² = y³ +9, do the following:

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Q: Find the distance from the point (2, 2, 3) to the line x = 0, y = 2+2t, z = 3+ t.

A: Find the distance from the point (2, 2, 3) to the line x= 0, y=2+2t, z=3+t.

Q: Plot z = sin(r)/r with r = Væ2 + y?, -8 < x < 8, -8 < y < 8.

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Q: Find the distance from the point (2, 2, 3) to the line x = 0, y = 2 + 2t, z = 3 + t.

A: Given point (2,2,3)and line is x=0 , y=2+2t ,z=3+t.

Q: Find point P(x,y) if it is equidistant between points A(2,9) and B(-3,6)

A: Given:-  Px,y is equidistant  from the points  A2,9  and  B -3,6 i.e,  AP=BP and  we know  that…

Q: Evaluate the slope at the point (2, 0) for: y² + sin(y) = 3x² - 12

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Q: 24=y cotx

A: Given differential equation is 2y'=ycotx.......1. We have to find the general solution of the given…