Question:
Given the system of straight lines
a(2x+y-3)+b(3x+2y-5)=0, the line of the system situated farthest from the point (4,-3) has the equation
Given the system of straight lines
a(2x+y-3)+b(3x+2y-5)=0, the line of the system situated farthest from the point (4,-3) has the equation
Show Hint
The farthest line from a point has the maximum perpendicular distance from that point.
Updated On: Mar 19, 2026
- 4x+y-15=0
- 7x+y-8=0
- 4x+3y-7=0
- 3x-4y+1=0
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: A general line of the system is
(2a+3b)x+(a+2b)y-(3a+5b)=0
Step 2: Distance of a line Ax+By+C=0 from point (x₀,y₀) is:
D=frac|Ax₀+By₀+C|√(A²+B²)
Step 3: Evaluating distances of given options from (4,-3), the maximum distance is obtained for:
3x-4y+1=0
Hence, option (D) is correct.
Was this answer helpful?
0
0
Top Questions on Straight lines
- Rhombus vertices A(1,2), C(-3,-6). Line AD parallel to $7x-y=14$. Find $|\alpha+\beta+\gamma+\delta|$.
- JEE Main - 2026
- Mathematics
- Straight lines
- Let the angles made with the positive $x$-axis by two straight lines drawn from the point $P(2,3)$ and meeting the line $x+y=6$ at a distance $\sqrt{\frac{2}{3}}$ from the point $P$ be $\theta_1$ and $\theta_2$. Then the value of $(\theta_1+\theta_2)$ is
- JEE Main - 2026
- Mathematics
- Straight lines
- If two lines drawn from a point $P(2,3)$ intersect the line $x+y=6$ at a distance $\sqrt{\dfrac{2}{3}}$, then the angle between the lines is
- JEE Main - 2026
- Mathematics
- Straight lines
- If two lines drawn from a point $P(2,3)$ intersect the line $x+y=6$ at a distance $\sqrt{\dfrac{2}{3}}$, then the angle between the lines is
- JEE Main - 2026
- Mathematics
- Straight lines
- Find the slope of the line perpendicular to the line $ 3x + 4y - 12 = 0 $.
- AP EAPCET - 2025
- Mathematics
- Straight lines
View More Questions
Questions Asked in BITSAT exam
- The 5th term of an AP is 20 and the 12th term is 41. Find the first term.
- BITSAT - 2025
- Arithmetic Progression
- A dust particle of mass 4 × 10⁻¹² mg is suspended in air under the influence of an electric field of 50 N/C directed vertically upwards. How many electrons were removed from the neutral dust particle? (g = 10 m/s²)
- BITSAT - 2025
- Electrostatics
- Calculate the electric field at a point due to a uniformly charged spherical shell.
- BITSAT - 2025
- Electrostatics
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Vector Algebra
- Calculate the de Broglie wavelength of an electron moving with a given velocity.
- BITSAT - 2025
- Wave Optics
View More Questions