Question:
The straight line \(5x+3ay+k=0\) with the slope \(\dfrac{10}{9}\) passing through the point \((4,8)\), then \(k=\)
The straight line \(5x+3ay+k=0\) with the slope \(\dfrac{10}{9}\) passing through the point \((4,8)\), then \(k=\)
Show Hint
For the line
\[
Ax+By+C=0,
\]
the slope is
\[
\boxed{m=-\frac{A}{B}}.
\]
Substitute the given point into the equation to determine the constant term.
Updated On: Jul 15, 2026
- \(12\)
- \(14\)
- \(16\)
- \(18\)
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Find the value of \(a\).
The given equation is
\[
5x+3ay+k=0.
\]
Its slope is
\[
m=-\frac{5}{3a}.
\]
Given,
\[
-\frac{5}{3a}=\frac{10}{9}.
\]
Hence,
\[
45=-30a
\]
\[
a=-\frac32.
\]
Step 2: Substitute the point \((4,8)\). Substituting \(a=-\dfrac32\), \[ 5x-\frac92y+k=0. \] Using the point \((4,8)\), \[ 5(4)-\frac92(8)+k=0 \] \[ 20-36+k=0 \] \[ k=16. \]
Step 3: Final conclusion. \[ \boxed{k=16} \] Hence, the correct option is \(\boxed{(C)}\).
Step 2: Substitute the point \((4,8)\). Substituting \(a=-\dfrac32\), \[ 5x-\frac92y+k=0. \] Using the point \((4,8)\), \[ 5(4)-\frac92(8)+k=0 \] \[ 20-36+k=0 \] \[ k=16. \]
Step 3: Final conclusion. \[ \boxed{k=16} \] Hence, the correct option is \(\boxed{(C)}\).
Was this answer helpful?
0
0
Top TG ICET Mathematical Ability Questions
- \[ \frac{\left(a^{\frac12}b^{-\frac16}\right)^3- \left(a^{\frac16}b^{\frac13}\right)^3} {a^{\frac12}-b^{\frac12}} = ? \]
- \[ 64^{\frac13} - 81^{\frac14} + 625^{\frac14} = ? \]
- If \(x:y=4:5\), then \((5x+4y):(10x-2y)=\ ?\)
- The ratio of milk and water in a can of 36 liters is \(3:1\). If 6 more liters of water is added, then the ratio of the milk and water will be:
- If \[ \sqrt{12+4\sqrt5} + \sqrt{16-4\sqrt7} = \sqrt{x}+\sqrt{y}, \] then find the value of \[ \sqrt{35xy}. \]
View More Questions
Top TG ICET Geometry Questions
- The least number of square tiles required to cover the floor of a room with dimensions \(24\) meters \(78\) cm \(\times\) \(27\) meters \(26\) cm is:
- What is the area of a rhombus (in sq.m.) whose perimeter is 40 m and one of its diagonals is 16 m?
- The dimensions of a brick and a wall are \(20\text{ cm} \times 10\text{ cm} \times 7.5\text{ cm}\) and \(25\text{ m} \times 2\text{ m} \times 0.75\text{ m}\) respectively. How many bricks (in thousands) are required to construct the wall?
- The volume of a cuboid is twice that of the volume of a cube. The dimensions of the cuboid are 9 cm, 8 cm, and 6 cm. If it costs ₹2.50 per sq.cm. for painting, the amount required to paint the surfaces of the cube (in rupees) is:
- The length and height of a godown are \(22\)m and \(6.5\)m respectively. If the area of four walls is \(442\) sq.m., then the breadth of the room in meters is:
View More Questions
Top TG ICET Questions
- What is the average of the integers 1, 2, 3, 4, and \(x\)? Statement (I): \(x\) is an even integer. Statement (II): \(x<10\)
- What is the average of \(x,y,z\) and \(t\)? Statement (I): \(x+z=12\) Statement (II): \(y+t=24\)
- What is the sum of the first 30 terms of an Arithmetic Progression? Statement (I): The common difference of the A.P. is 5. Statement (II): The first and the last terms are 2 and 60 respectively.
- In triangle \(ABC\), is \(\angle A\) obtuse? Statement (I): \(\angle C\) is acute. Statement (II): \(\angle B\) is obtuse.
- What is the circumference of the regular hexagon? Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm. Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
View More Questions