If the line (x / a) + (y / b) = 1 moves in such a way that (1/a²) + (1/b²) = (1/ c²) where c is a constant, prove that the foot of the perpendicular from the origin on the straight line describes the x² + y² = C

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A: Solution: Let the point P(x,y) is the position of Ant and given that the distance from P(x,y) to…

Q: Find the point on the line x - 3y+9 = 0 that is closest to the point (-1, 3). 1) (-0.9, 2.7) O 2)…

A: Closest distance form a point to a line is normal distance from point to line.

Q: a point Q(x2, y2) is on the line segment passing through R(-2,5) and S(4,1). Find the coordinates of…

A: Given: Given that the point Qx,y is on the line segment passing through R-2,5 and S4,1 Point Q is…

Q: #3 Find the line equation(s) of the line(s) through point P(1, 0, 1) that meets the following line…

A: Given :  Given:P(1,0,1)L: x,y,x=1,2,0+t2,-1,2P0=1,2,0Aim: To find a line(s) through point P,…

Q: Find an equation of the line through (-2, 5, 3) that is perpendicular to both u = (1, 1, 2) and the…

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Q: Find a point whose coordinates are integers and whose distance from (3, 2) is √41

A: To find:   a point whose coordinates are integers and whose distance from (3, 2) is √41 Consider the…

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: Sketch the line parallel to 3x + 2y = 12 which passes through the point P(0, 2).

A: Given,         The line parallel to 3x+2y=12 which passes through the point P0,2.We know that,…

Q: A point P(x, y) moves so that the sum of the squares of its distances from points A(0,0)and B(2,-4)…

A: Given,           A point P(x, y) moves so that the sum of the squares of its distances from points…

Q: A company’s profit increased linearly from $6million at the end of year 1 to $14 million at the end…

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Q: i 6i + 2j+ 2k + 2(i- 2j+2k) Find the shortest distance between lines -4i -i + 4(3i - 2)- 2k) and

A: The given lines are as follows- r→=6i^+2j^+λi^-2j^+2k^          ........(1)r→=-4i^-k^+μ3i^-2j^-2k^…

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Q: Find the distance between the point (2, 9) and the line y = 3x + 4

A: Find the distance between the point (2, 9) and the line y = 3x + 4 To find the distance between a…

Q: Show that the point (x0 , y0) closest to the origin on the line ax+ by =c has coordinates

A: Distance between x0, y0 and origin (0, 0) is, D=x0-02+y0-02D=x02+y02D2=x02+y02f=x02+y02…

Q: Find the distance from the point (-7,-8,5) to the line ä(t) =(2, 5, 3)t + (-1, 3, 4).

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Q: If A = ( - 1, 2) and B = (3, 4), find AB and redraw it (a) in standard position and(b) with its tail…

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Q: A billiards table is 8 feet by 4 feet, and has pockets in all four corners and in the middle of the…

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