Advertisements
Advertisements
प्रश्न
A point equidistant from the line 4x + 3y + 10 = 0, 5x − 12y + 26 = 0 and 7x+ 24y − 50 = 0 is
विकल्प
(1, −1)
(1, 1)
(0, 0)
(0, 1)
उत्तर
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
संबंधित प्रश्न
The line through the points (h, 3) and (4, 1) intersects the line 7x – 9y – 19 = 0. at right angle. Find the value of h.
Find the equations of the lines, which cut-off intercepts on the axes whose sum and product are 1 and –6, respectively.
If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m3x + c3 are concurrent, then show that m1(c2 – c3) + m2 (c3 – c1) + m3 (c1 – c2) = 0.
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.
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 equation of a line which makes an angle of tan−1 (3) with the x-axis and cuts off an intercept of 4 units on negative direction of y-axis.
Find the equation of a line that has y-intercept −4 and is parallel to the line joining (2, −5) and (1, 2).
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 (3, 4) and (−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 equation of a line for p = 5, α = 60°.
Find the equation of a line for p = 8, α = 225°.
Find the equation of the straight line on which the length of the perpendicular from the origin is 2 and the perpendicular makes an angle α with x-axis such that sin α = \[\frac{1}{3}\].
Find the equation of the straight line upon which the length of the perpendicular from the origin is 2 and the slope of this perpendicular is \[\frac{5}{12}\].
Reduce the equation \[\sqrt{3}\] x + y + 2 = 0 to slope-intercept form and find slope and y-intercept;
Reduce the equation\[\sqrt{3}\] x + y + 2 = 0 to intercept form and find intercept on the axes.
Reduce the following equation to the normal form and find p and α in x − 3 = 0.
Show that the origin is equidistant from the lines 4x + 3y + 10 = 0; 5x − 12y + 26 = 0 and 7x + 24y = 50.
Find the values of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line \[\sqrt{3}x + y + 2 = 0\].
Find the point of intersection of the following pairs of lines:
\[y = m_1 x + \frac{a}{m_1} \text { and }y = m_2 x + \frac{a}{m_2} .\]
Find the equations of the medians of a triangle, the equations of whose sides are:
3x + 2y + 6 = 0, 2x − 5y + 4 = 0 and x − 3y − 6 = 0
Prove that the lines \[y = \sqrt{3}x + 1, y = 4 \text { and } y = - \sqrt{3}x + 2\] form an equilateral triangle.
Find the equation of the straight line perpendicular to 2x − 3y = 5 and cutting off an intercept 1 on the positive direction of the x-axis.
Find the coordinates of the foot of the perpendicular from the point (−1, 3) to the line 3x − 4y − 16 = 0.
Find the values of α so that the point P (α2, α) lies inside or on the triangle formed by the lines x − 5y+ 6 = 0, x − 3y + 2 = 0 and x − 2y − 3 = 0.
Write the coordinates of the orthocentre of the triangle formed by the lines x2 − y2 = 0 and x + 6y = 18.
If a ≠ b ≠ c, write the condition for which the equations (b − c) x + (c − a) y + (a − b) = 0 and (b3 − c3) x + (c3 − a3) y + (a3 − b3) = 0 represent the same line.
The point which divides the join of (1, 2) and (3, 4) externally in the ratio 1 : 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 a line which passes through the point (2, 3) and makes an angle of 30° with the positive direction of x-axis.
Prove that every straight line has an equation of the form Ax + By + C = 0, where A, B and C are constants.
Find the equation of the straight line which passes through the point (1, – 2) and cuts off equal intercepts from axes.
The line which cuts off equal intercept from the axes and pass through the point (1, –2) is ______.
