Question:
Two lines \( x - y + 1 = 1 \) and \( x - 3y - k = 2 \) intersect at a point, if \( k \) is equal to?
Two lines \( x - y + 1 = 1 \) and \( x - 3y - k = 2 \) intersect at a point, if \( k \) is equal to?
Show Hint
To find the point of intersection of two lines, solve their equations simultaneously.
Updated On: Jan 12, 2026
- \( \frac{1}{4} \)
- \( 1 \)
- \( -4 \)
- None of these
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
To find the value of \( k \) where the lines intersect, substitute the values of \( x \) and \( y \) from one equation into the other, then solve for \( k \).
Was this answer helpful?
0
0
Top Questions on Coordinate Geometry
- Consider a circle \(C_1\), passing through origin and lying in region \(0 \le x\) only, with diameter = 10. Consider a chord \(PQ\) of \(C_1\) with equation \(y = x\) and another Circle \(C_2\) which has \(PQ\) as diameter. A chord is drawn to \(C_2\) passing through (2, 3) such that distance of chord from centre of \(C_2\) is maximum has equation \(x + ay + b = 0\) then \(|b - a|\) is equal to :
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- Orthocentre of equilateral \(\Delta ABC\) is at the origin. If side \(BC\) lies along \(x + 2\sqrt{2}y = 4\). If coordinates of vertex \(A\) are (a,b). Find the value of \(\lfloor |a + \sqrt{2}b| \rfloor\), where \([ \cdot ]\) denotes G.I.F. :
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- Given conic \(x^2 - y^2 \sec^2 \theta = 8\) whose eccentricity is '\(e_1\)' & length of latus rectum '\(l_1\)' and for conic \(x^2 + y^2 \sec^2 \theta = 6\), eccentricity is '\(e_2\)' & length of latus rectum '\(l_2\)'. If \(e_1^2 = e_2^2 (1 + \sec^2 \theta)\) then value of \(\frac{e_1 l_1}{e_2 l_2} \tan \theta\)
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- Let \( \frac{x^2}{2} + \frac{y^2}{1} = 1 \) and \( y = x + 1 \) intersect each other at points A & B, then \( \angle AOB \) (where O is the centre of the ellipse) is:
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
- Let \( A(1, 6, 3) \) and point \( B \) and \( C \) lie on the line \[ \frac{x - 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{3} \] where \( B(4, 9, \alpha) \) and point \( C \) is 10 units from \( B \). Find the area of \( \triangle ABC \):
- JEE Main - 2026
- Mathematics
- Coordinate Geometry
View More Questions
Questions Asked in VITEEE exam
- Find the value of \( x \) in the following equation: \[ \frac{2}{x} + \frac{3}{x + 1} = 1 \]
- VITEEE - 2025
- Algebra
- In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
- VITEEE - 2025
- Data Interpretation
- TUV : VYB :: PRA : ?
- VITEEE - 2025
- Odd one Out
- What is the pH of a solution with a \( \text{H}^+ \) concentration of \( 1 \times 10^{-3} \) mol/L?
- VITEEE - 2025
- Solubility Equilibria Of Sparingly Soluble Salts
- In a code language, 'TIGER' is written as 'JUISF'. How will 'EQUAL' be written in that language?
- VITEEE - 2025
- Odd one Out
View More Questions