The lines joining the origin to the point of intersection of the line lx+my=1 and y²=4ax are at right angles. Show that 4al=1

Q: Construct a line perpendicular to the line below through point W. W

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Q: Write the equations of the lines tangent to the circle (x + 3)² + (y – 4)² = 18 and are…

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Q: Show that the product of the perpendicular distances from the origin to the pair of lel la-b) + 4h?…

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Q: calculate the distance between point(5,2) and the line, 2x+5y=10

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Q: Where is the line y = 10 – 2x closest to the origin? (х, у) %3D

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Q: Find the Point). tongent line is ho FLx) =X %3D

A: given

Q: Find the distance from the point (3,4,1) to the line x=0, y= 4+2t, z= 1+t

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Q: When is the line ax+ by = c parallel to the y-axis? To the x-axis?

A: ax+by+c=0        When a=0, then the line equation becomes               bx+c=0…

Q: Find the envelope of the family of straight lines, which together with the line segments intercepted…

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Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x, y) = |

A: To find - Point on the given line closest to the origin.

Q: Find the angle from the line 9y – 5x + 23 = 0 to the vertical line 6 units from the y – axis. Angles…

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Q: Construct a line perpendicular to the line given through the point P at the right.

A: To plot the line perpendicular to the given line through the point P

Q: Find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 + 4t

A: To find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 +…

Q: Find the distance of the point (2, 2, –5) from the line r(t) = (1+4t, –1+ 4t,7 – 3t) %3D swer:

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Q: If a line intersects the x-axis at 'r' and the y-axis at '1/r', at what point (x,y) does it…

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Q: Find distance from the point (0, 1, 3) to the line = 2t, y = 6–2t, z = 3+t

A: (0,1,3)    L=x=2t, y=6-2t, z=3+t

Q: Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is the slope of the…

A: Here ABCD is a trapezoid and AB parallel BC which also parallel to the X axis

Q: In the figures, ʘA and ʘB are intersected by tangent lines while ʘC and ʘD are intersected by secant…

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Q: Find the distance between the point (−3, 5, 1) and the line given by x = 1 + t, y = 5 − 2t, and z =…

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Q: Two straight lines 3x – 2 y + 5 = 0 and 6x – 4y + 10 = 0 intersect at the origin. are coincident.…

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Q: The distance from a point (2, y) to the line 4x + 3y =0 is equal to 5. Find the value of y.

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Q: ) Find the distance from the point (4, 1, 2) to the line x = 0, y = 1+ 5t, z = 2+ t.

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Q: Find the point on the line y=5x+3 that is closest to the origin (x,y)=(______)

A: Let (m,n) be the point on the line which is closest to the origin.Put n = m, y = n, in y = 5x + 3…

Q: Find the distance from the point P(2,1) to the line v = x + 2

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Q: Find the point on the line y = 2x + 3 that is closest to the origin. (x, y) =

A: The perpendicular drawn from the origin to the line represents the shortest distance.

Q: d the eqation of the line that passes through A(1,2,1) and intersects the line x+1 у-2 z+1 %3D at…

A: Topic:- geometry

Q: The slope of the line tangent to the circle x' + y = 100 at the point (- 6,8)is

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Q: Find the distance from the point (4, 1, 2) to the line x = 0, y = 1+ 5t, Z = 2 + t.

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Q: Find the distance from the point (1, 5, 5) to the line x = 0, y = 5 + t, z = 5 + 5t.

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Q: construct a line that goes through point A and is perpendicular to a line.

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Q: With center on the line y = 2x – 13 and tangent to the line y = - 3x + 57 at (16, 9)

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Q: Find the distance between the two straight lines and x=1+1, y=2, z= −1+2+ x=2-t, y=3t4t, z=2t at the…

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Q: Find the point on the line y = 3x + 2 that is closest to the origin. (х, у) %3D

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Q: Line l is an auxiliary line parallel to m

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Q: Find the point on the line y = 4x + 3 that is closest to the origin. (x, y) =

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Q: Two straight lines 3x - 2y + 5 = 0 and 6x - 4y + 10 = 0 intersect at the origin. are coincident. are…

A: This question is based on straight line intersection.

Q: In the xy-plane, line k intersects the y-axis at the point (0, –6) and passes through the point (2,…

A: Given:- In the xy-plane, line k intersects the y-axis at the point (0, -6) and passes through the…

Q: Find the point on the line y = 3x + 4 that is closest to the origin. (x,y)=

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Q: 2)What line is perpendicular to 2x + y = 3 at (1,1)?

A: What line is perpendicular to 2x+y=3 at (1,1)?

Q: What can you conclude if you know that the point (p, q) lies on the line y = mx + b?

A: We have to conclude if the point p, q lies on the line y=mx+b. We know that if any point is lying on…

Q: find point b (x,y) given that M (7,3) is the midpoint of line A(10,4) and b

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Q: Construct perpendicular lines from point P to line m. 1. VE

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: The students in Ms. Logan’s class were asked to construct a line perpendicular to line through point…

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Q: Find the distance between parallel lines 8x + 15y + 18 = 0 and 8x + 15y + 1 = 0

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Q: Find the distance between the line x + y + 2 = 0 and the point (1, 1).

A: The distance between the line ax+by+c=0 and the point x1,y1 is given as below. d=ax1+by1+ca2+b2

Q: ez ds where C is the line segment from (0, 6,-1) to (4, , 5). Compute

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Q: The midpoint of the line segment between P1 (x,y) and P2 (-2,4) is Pm (2,-1). Find the coordinates…

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Q: george noticed when that pair of paralell lines was cut by a transversal, a certain pair of adjacent…

A: We have to find the conclusion when pair of parallel lines are cut by a transversal and a certain…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.