Advertisements
Advertisements
Question
A point equidistant from the line 4x + 3y + 10 = 0, 5x − 12y + 26 = 0 and 7x+ 24y − 50 = 0 is
Options
(1, −1)
(1, 1)
(0, 0)
(0, 1)
Solution
Let the coordiantes of the point be (a, b)
Now, the distance of the point (a, b) from 4x + 3y + 10 = 0 is given by
\[\left| \frac{4a + 3b + 10}{\sqrt{4^2 + 3^2}} \right|\]
\[ = \left| \frac{4a + 3b + 10}{5} \right|\]
Again, the distance of the point (a, b) from 5x − 12y + 26 = 0 is given by
\[\left| \frac{5a - 12b + 26}{\sqrt{5^2 + \left( - 12 \right)^2}} \right|\]
\[ = \left| \frac{5a - 12b + 26}{13} \right|\]
Again, the distance of the point (a, b) from 7x + 24y − 50 = 0 is is given by
\[\left| \frac{7a + 24b - 50}{\sqrt{7^2 + \left( 24 \right)^2}} \right|\]
\[ = \left| \frac{7a + 24b - 50}{25} \right|\]
Now,
\[\left| \frac{4a + 3b + 10}{5} \right| = \left| \frac{5a - 12b + 26}{13} \right| = \left| \frac{7a + 24b - 50}{25} \right|\]
Only a = 0 and b = 0 is satisfying the above equation
Hence, the correct answer is option (c).
APPEARS IN
RELATED QUESTIONS
Reduce the following equation into intercept form and find their intercepts on the axes.
3y + 2 = 0
Find equation of the line parallel to the line 3x – 4y + 2 = 0 and passing through the point (–2, 3).
Prove that the line through the point (x1, y1) and parallel to the line Ax + By + C = 0 is A (x –x1) + B (y – y1) = 0.
Two lines passing through the point (2, 3) intersects each other at an angle of 60°. If slope of one line is 2, find equation of the other line.
If p and q are the lengths of perpendiculars from the origin to the lines x cos θ – y sin θ = k cos 2θ and xsec θ+ y cosec θ = k, respectively, prove that p2 + 4q2 = k2.
Find the equation of the line passing through the point of intersection of the lines 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.
Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0 and 3x + 2y + 6 = 0.
The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (−4, 1). Find the equation of the legs (perpendicular sides) of the triangle that are parallel to the axes.
Find the equation of a line making an angle of 150° with the x-axis and cutting off an intercept 2 from y-axis.
Find the lines through the point (0, 2) making angles \[\frac{\pi}{3} \text { and } \frac{2\pi}{3}\] with the x-axis. Also, find the lines parallel to them cutting the y-axis at a distance of 2 units below the origin.
Find the equation of the right bisector of the line segment joining the points A (1, 0) and B (2, 3).
Find the equation of the side BC of the triangle ABC whose vertices are (−1, −2), (0, 1) and (2, 0) respectively. Also, find the equation of the median through (−1, −2).
For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x − 3y + 6 = 0 on the axes.
Find the value of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line \[\sqrt{3}x + y + 2 = 0\].
Reduce the following equation to the normal form and find p and α in x − 3 = 0.
Reduce the following equation to the normal form and find p and α in y − 2 = 0.
Reduce the lines 3 x − 4 y + 4 = 0 and 2 x + 4 y − 5 = 0 to the normal form and hence find which line is nearer to the origin.
Find the coordinates of the vertices of a triangle, the equations of whose sides are x + y − 4 = 0, 2x − y + 3 = 0 and x − 3y + 2 = 0.
Find the equation of the line joining the point (3, 5) to the point of intersection of the lines 4x + y − 1 = 0 and 7x − 3y − 35 = 0.
For what value of λ are the three lines 2x − 5y + 3 = 0, 5x − 9y + λ = 0 and x − 2y + 1 = 0 concurrent?
Show that the straight lines L1 = (b + c) x + ay + 1 = 0, L2 = (c + a) x + by + 1 = 0 and L3 = (a + b) x + cy + 1 = 0 are concurrent.
Find the equation of the straight line which has y-intercept equal to \[\frac{4}{3}\] and is perpendicular to 3x − 4y + 11 = 0.
Find the equation of the right bisector of the line segment joining the points (a, b) and (a1, b1).
Find the values of the parameter a so that the point (a, 2) is an interior point of the triangle formed by the lines x + y − 4 = 0, 3x − 7y − 8 = 0 and 4x − y − 31 = 0.
Write the coordinates of the orthocentre of the triangle formed by the lines xy = 0 and x + y = 1.
If the lines ax + 12y + 1 = 0, bx + 13y + 1 = 0 and cx + 14y + 1 = 0 are concurrent, then a, b, c are in
The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (−2, 6). The third vertex is
Find the equation of the lines which passes through the point (3, 4) and cuts off intercepts from the coordinate axes such that their sum is 14.
A line cutting off intercept – 3 from the y-axis and the tangent at angle to the x-axis is `3/5`, its equation is ______.
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is (3, 2), then the equation of the line will be ______.
For specifying a straight line, how many geometrical parameters should be known?
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is ______.
Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.
x + 7y = 0
Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.
y = 0
Reduce the following equation into intercept form and find their intercepts on the axes.
3x + 2y – 12 = 0
