Find All Points On x + y = 4 That Lie At A Unit Distance From The Line 4x + 3y– 10 = 0.

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Question

Find all points on x + y = 4 that lie at a unit distance from the line 4x + 3y– 10 = 0.

Solution

Correct option is

(–7, 11) and (3, 1)

Let P (t, 4 – t) be an arbitrary point on the line x + y = 4.  

Distance of P from 4x + 3y – 10 = 0 is unity.

   

⇒       Points are (–7, 11) and (3, 1).

Testing

SIMILAR QUESTIONS

Q1

The image of point (1, 3) in the line x + y – 6 = 0 is: 

Q2

If t1t2t3 are distinct, then the points  are collinear if:

Q3

A and B are two fixed points. The vertex C of a Δ ABC moves such that cot A + cot B = constant. Locus of C is a straight line:

Q4

The number of integer values of m, for which the x-co-ordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer, is:

Q5

The vertices of a triangles are A (x1x1 tan α), B (x2x2 tan β) and C (x3,x3 tan γ). If the circumcentre of Δ ABC coincides with the origin and H (ab) be its orthocenter, then a/b is equal to:

Q6

A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinates axes at points P and Q. As L varies, the absolute minimum values of OP + OQ is (O is origin)

 

 

Q7

Consider the family of lines 

           (x + y – 1) + λ (2x + 3y – 5) = 0

and   (3x + 2y – 4) + µ (x + 2y – 6) = 0  

equation of a straight line that belongs to both the families is:

Q8

If p1p2p3 be the length perpendicular from the points

(m2, 2m), (mm’m + m’) and (m’2, 2m’)

respectively on the line  

               

Q9

The point (a2a + 1) is a point in the angle between the lines 3x – y + 1 = 0 and x + 2y – 5 = 0 containing origin. Then ‘a’ belongs to the interval. 

Q10

Find the equation of the obtuse angle bisector of the lines 12x – 5y + 7 = 0 and 3y – 4x – 1 = 0.